Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -3

 

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -3

Section A: Angles & Types of Angles (10 Questions)

1. What is the correct name for an angle that is greater than 180° but less than 360°?

2. Look at the clock. What type of angle is between the hands at 2 o'clock?

3. An angle is measured at 91°. What type of angle is it?

4. How many right angles are there in a full turn?

5. Two angles are complementary. One is 37°. What is the other?

6. An angle is half the size of its supplement. What is the size of the smaller angle?

7. In a triangle, one angle is a right angle and another is 30°. What is the third angle?

8. A reflex angle is 245°. What is the size of the corresponding acute/obtuse angle inside the shape?

9. Which of these is not possible for the angles of a triangle? A) 45°, 55°, 80° B) 60°, 60°, 60° C) 100°, 40°, 40° D) 30°, 70°, 100°

10. A full rotation is divided into 5 equal angles. How big is each angle?

Section B: Polygons (10 Questions)

11. What is the sum of the interior angles of a heptagon?

12. A regular polygon has an exterior angle of 24°. How many sides does it have?

13. The interior angles of a pentagon are 100°, 110°, 115°, 105° and *x*. Find the value of *x*.

14. What is the name of a nine-sided polygon?

15. Is it possible for a regular polygon to have an interior angle of 170°? Explain your answer.

16. How many diagonals can you draw from one vertex of a hexagon?

17. The sum of the interior angles of a polygon is 1260°. How many sides does it have?

18. A regular octagon has how many lines of symmetry?

19. Each interior angle of a regular polygon is 144°. What is the name of the polygon?

20. True or False: A circle is a polygon.

Section C: Properties of 2D Shapes (50 Questions)

This section covers Triangles and Quadrilaterals (sides, angles, symmetry).

21. What type of triangle has all sides different lengths?

22. A triangle has angles of 70° and 70°. What is the size of the third angle and what type of triangle is it?

23. How many lines of symmetry does an equilateral triangle have?

24. What is the order of rotational symmetry of a square?

25. Which quadrilateral has only one pair of parallel sides?

26. All squares are rectangles. Are all rectangles squares?

27. A rhombus has all sides equal. Does it always have all angles equal?

28. What is the specific name for a quadrilateral with both pairs of opposite sides parallel and equal?

29. A parallelogram has one angle of 75°. What are the sizes of its other three angles?

30. How many right angles does a kite have?

31. What is the difference between a scalene and an isosceles triangle?

32. Draw a sketch of a trapezium.

33. A triangle has one line of symmetry and no rotational symmetry. What type of triangle is it?

34. True or False: A rhombus is a regular polygon.

35. What is the size of each angle in an equilateral triangle?

36. A quadrilateral has rotational symmetry of order 4. What could it be?

37. How many pairs of equal sides does an isosceles triangle have?

38. What is the sum of the angles in any quadrilateral?

39. A shape has four lines of symmetry and rotational symmetry of order 4. What is it?

40. True or False: Every square is a rhombus.

41. In an isosceles triangle, the angle at the apex (top) is 40°. What is the size of each base angle?

42. A rectangle has a length of 8cm and a width of 5cm. What is the perimeter?

43. A square has a perimeter of 36cm. What is its area?

44. A parallelogram has an area of 20cm² and a base of 5cm. What is its height?

45. A triangle is drawn on a centimetre grid. Its vertices are at (1,1), (1,5), and (4,1). What is its area?

46. What is the name given to the longest side of a right-angled triangle?

47. If two angles in a triangle are 45° and 55°, what is the third angle and what type of triangle is it?

48. A quadrilateral has exactly two lines of symmetry. It is not a rectangle. What could it be?

49. How many sides does a heptagon have?

50. True or False: A trapezium can have a right angle.

51. A regular polygon has an interior angle of 135°. How many sides does it have?

52. What is the exterior angle of a regular nonagon?

53. A triangle has sides of length 5cm, 5cm, and 8cm. What type of triangle is it?

54. A triangle has sides of length 3cm, 4cm, and 5cm. What type of triangle is it?

55. A quadrilateral has all sides equal and one angle of 90°. What is its name?

56. A quadrilateral has opposite angles equal and all sides equal, but it is not a square. What is it?

57. How many lines of symmetry does a regular hexagon have?

58. What is the order of rotational symmetry of an equilateral triangle?

59. True or False: A circle has infinite lines of symmetry.

60. A shape has rotational symmetry of order 2 and no line symmetry. What could it be?

61. A triangle has an area of 15cm² and a base of 6cm. What is its height?

62. A square has an area of 49cm². What is its perimeter?

63. A rectangle has a perimeter of 24cm and a length of 8cm. What is its width?

64. A parallelogram has a base of 10cm and a height of 3cm. What is its area?

65. A trapezium has parallel sides of 6cm and 10cm, and a height of 4cm. What is its area?

66. What is the name of a triangle with all angles less than 90°?

67. What is the name of a triangle with one angle greater than 90°?

68. True or False: A rhombus has diagonals that bisect each other at right angles.

69. How many vertices does a pentagon have?

70. What is the name of a quadrilateral where diagonals are equal and bisect each other at right angles?

Section D: Angle Rules (30 Questions)

*Apply these rules: Straight line=180°, Around a point=360°, Vertically opposite are equal, Triangle sum=180°, Quadrilateral sum=360°.*

71. Two angles on a straight line are 125° and *x*. Find *x*.

72. Three angles around a point are 100°, 150° and *y*. Find *y*.

73. In the diagram, two straight lines cross. One angle is 40°. What are the sizes of the other three angles?

74. In an isosceles triangle, the vertex angle is 50°. What is the size of each base angle?

75. A quadrilateral has angles of 80°, 95°, and 110°. What is the fourth angle?

76. Find the size of angle *a* in a triangle with angles 60° and 70°.

77. Angles *p* and *q* are vertically opposite. If *p* is 110°, what is *q*?

78. In a right-angled triangle, one acute angle is twice the other. What are the sizes of the angles?

79. A straight line has three angles on it, *x*, 2*x*, and 90°. Find the value of *x*.

80. In a parallelogram, one angle is 110°. What are the sizes of the other three angles?

81. The angles of a triangle are in the ratio 2:3:4. Find the size of the largest angle.

82. In a rhombus, one angle is 65°. What is the size of the angle adjacent to it?

83. Angles *a* and *b* are on a straight line. Angle *a* is 3 times angle *b*. Find angle *b*.

84. Four angles around a point are 2*x*, 3*x*, 4*x*, and 5*x*. Find the value of *x*.

85. In a pentagon, four of the angles are 100°, 110°, 120°, and 130°. What is the fifth angle?

86. An isosceles triangle has a base angle of 40°. What is the vertex angle?

87. Two angles in a triangle are 35° and 45°. What is the third angle?

88. In a quadrilateral, three angles are equal and the fourth is 90°. What is the size of each of the equal angles?

89. Angles *c* and *d* are complementary. Angle *c* is 15° more than angle *d*. Find angle *c*.

90. The exterior angle of a triangle is 120° and one of its interior opposite angles is 50°. What is the other interior opposite angle?

91. In a trapezium with one pair of parallel sides, one angle is 85°. What is the angle on the same side of the transversal?

92. A triangle has angles of (x+10)°, (2x-20)°, and 60°. Find the value of x.

93. A quadrilateral has angles of x, 2x, 3x, and 4x. Find the value of x.

94. In a regular hexagon, what is the size of each interior angle?

95. The angles of a triangle are (2y)°, (3y)°, and (4y)°. Find the value of y.

96. On a straight line, angles are 2a, 3a, and 4a. Find the smallest angle.

97. Around a point, angles are a, 2a, 3a, 4a, and 5a. Find the largest angle.

98. In an isosceles triangle, the vertex angle is 4 times a base angle. Find the vertex angle.

99. Two vertically opposite angles are (3x+10)° and (5x-20)°. Find the value of x.

100. In a right-angled isosceles triangle, what are the sizes of the two acute angles?

ANSWER KEY

Section A: Angles & Types of Angles

1. What is the correct name for an angle that is greater than 180° but less than 360°?
Answer: Reflex angle
Explanation: Angles are classified as acute (< 90°), right (90°), obtuse (between 90° and 180°), reflex (between 180° and 360°), and full turn (360°). Therefore, an angle between 180° and 360° is a reflex angle.

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2. Look at the clock. What type of angle is between the hands at 2 o’clock?
Answer: Acute
Explanation: At 2 o’clock, the hour hand is at 2 and the minute hand is at 12. The angle between each hour mark on a clock is 30° (360° ÷ 12 = 30°). From 12 to 2 is 2 × 30° = 60°, which is less than 90°, so it is acute.

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3. An angle is measured at 91°. What type of angle is it?
Answer: Obtuse
Explanation: An obtuse angle is greater than 90° and less than 180°. Since 91° lies in that range, it is obtuse.

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4. How many right angles are there in a full turn?
Answer: 4
Explanation: A full turn is 360°. A right angle is 90°. 360° ÷ 90° = 4.

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5. Two angles are complementary. One is 37°. What is the other?
Answer: 53°
Explanation: Complementary angles add up to 90°. So, 90° − 37° = 53°.

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6. An angle is half the size of its supplement. What is the size of the smaller angle?
Answer: 60°
Explanation: Let the smaller angle be $x$. Its supplement is $2x$. Supplementary angles add to 180°, so $x+2x=180\mathrm{°}$, giving $3x=180\mathrm{°}$ and $x=60\mathrm{°}$.

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7. In a triangle, one angle is a right angle and another is 30°. What is the third angle?
Answer: 60°
Explanation: The sum of angles in a triangle is 180°. 180° − (90° + 30°) = 60°.

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8. A reflex angle is 245°. What is the size of the corresponding acute/obtuse angle inside the shape?
Answer: 115°
Explanation: The corresponding angle inside a full rotation is 360° − reflex angle. 360° − 245° = 115°, which is obtuse.

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9. Which of these is not possible for the angles of a triangle?
A) 45°, 55°, 80°
B) 60°, 60°, 60°
C) 100°, 40°, 40°
D) 30°, 70°, 100°

Answer: D) 30°, 70°, 100°
Explanation: The angles in a triangle must sum to 180°. Option D sums to 200°, so it is not possible.

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10. A full rotation is divided into 5 equal angles. How big is each angle?
Answer: 72°

Explanation: Full rotation = 360°. Divided into 5 equal parts: 360° ÷ 5 = 72°.

Section B: Polygons

11. What is the sum of the interior angles of a heptagon?
Answer: 900°
Explanation: A heptagon has 7 sides. The formula for the sum of interior angles is $(n-2)\times {180}^{\circ }$, where $n$ is the number of sides. So, $(7-2)\times {180}^{\circ }=5\times {180}^{\circ }={900}^{\circ }$.

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12. A regular polygon has an exterior angle of 24°. How many sides does it have?
Answer: 15 sides
Explanation: For any regular polygon, the sum of exterior angles is 360°. The number of sides is ${360}^{\circ }÷\text{exterior angle}$. So, ${360}^{\circ }÷{24}^{\circ }=15$.

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13. The interior angles of a pentagon are 100°, 110°, 115°, 105° and *x*. Find the value of *x*.
Answer: 110°
Explanation: A pentagon has 5 sides, so the sum of interior angles = $(5-2)\times {180}^{\circ }=3\times {180}^{\circ }={540}^{\circ }$. The given angles sum to $100+110+115+105={430}^{\circ }$. Therefore, $x={540}^{\circ }-{430}^{\circ }={110}^{\circ }$.

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14. What is the name of a nine-sided polygon?
Answer: Nonagon
Explanation: Standard polygon names: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10), etc.

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15. Is it possible for a regular polygon to have an interior angle of 170°? Explain your answer.
Answer: Yes
Explanation: If interior angle = 170°, then exterior angle = 180° - 170° = 10°. The number of sides would be ${360}^{\circ }÷{10}^{\circ }=36$. Since 36 is a whole number, a regular 36-sided polygon (triacontakaihexagon) is possible.

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16. How many diagonals can you draw from one vertex of a hexagon?
Answer: 3
Explanation: A hexagon has 6 vertices. From one vertex, you cannot draw a diagonal to itself or to the two adjacent vertices (they are already connected by sides). So diagonals = $6-3=3$.

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17. The sum of the interior angles of a polygon is 1260°. How many sides does it have?
Answer: 9 sides
Explanation: Using $(n-2)\times {180}^{\circ }={1260}^{\circ }$.
$n-2=1260÷180=7$
$n=7+2=9$.

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18. A regular octagon has how many lines of symmetry?
Answer: 8
Explanation: A regular octagon has 8 equal sides and 8 equal angles, so it has 8 lines of symmetry (through opposite vertices and through midpoints of opposite sides).

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19. Each interior angle of a regular polygon is 144°. What is the name of the polygon?
Answer: Decagon
Explanation: If interior = 144°, exterior = 180° - 144° = 36°. Number of sides = ${360}^{\circ }÷{36}^{\circ }=10$. A 10-sided polygon is a decagon.

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20. True or False: A circle is a polygon.
Answer: False
Explanation: A polygon is a closed shape with straight sides. A circle has a curved boundary, so it is not a polygon

Section C: Properties of 2D Shapes (First 20 of the 50 questions)

21. What type of triangle has all sides different lengths?
Answer: Scalene triangle
Explanation: Triangles are classified by side lengths:

• Equilateral: all sides equal

• Isosceles: two sides equal

• Scalene: all sides different

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22. A triangle has angles of 70° and 70°. What is the size of the third angle and what type of triangle is it?
Answer: 40°, isosceles triangle
Explanation: Sum of angles = 180°. Third angle = 180° - (70° + 70°) = 40°. Since two angles are equal, the sides opposite them are equal → isosceles triangle.

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23. How many lines of symmetry does an equilateral triangle have?
Answer: 3
Explanation: An equilateral triangle has three equal sides and three equal angles. Each line from a vertex to the midpoint of the opposite side is a line of symmetry → 3 lines.

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24. What is the order of rotational symmetry of a square?
Answer: 4
Explanation: A square fits onto itself 4 times during a full 360° rotation (at 90°, 180°, 270°, and 360°).

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25. Which quadrilateral has only one pair of parallel sides?
Answer: Trapezium (UK definition)
Explanation: In UK geometry:

• Trapezium: 1 pair of parallel sides

• Trapezoid (US): 1 pair of parallel sides

• Parallelogram: 2 pairs of parallel sides

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26. All squares are rectangles. Are all rectangles squares?
Answer: No
Explanation: A square is a special rectangle with all sides equal. Rectangles have opposite sides equal but not necessarily all four sides equal.

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27. A rhombus has all sides equal. Does it always have all angles equal?
Answer: No
Explanation: A rhombus has all sides equal, but angles are only equal if it's a square. A "slanted" rhombus has unequal opposite angles.

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28. What is the specific name for a quadrilateral with both pairs of opposite sides parallel and equal?
Answer: Parallelogram
Explanation: Definition of a parallelogram: both pairs of opposite sides are parallel (and therefore equal in length).

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29. A parallelogram has one angle of 75°. What are the sizes of its other three angles?
Answer: 75°, 105°, 105°
Explanation: In a parallelogram:

• Opposite angles are equal → another 75°

• Adjacent angles are supplementary (add to 180°) → 180° - 75° = 105° for the other two angles

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30. How many right angles does a kite have?
Answer: Typically 0, but can have 2 in a special case (right kite)
Explanation: A standard kite has no right angles unless specified as a "right kite," which has two opposite right angles.

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31. What is the difference between a scalene and an isosceles triangle?
Answer: Scalene has all sides different; isosceles has at least two equal sides.
Explanation: Classification by sides:

• Scalene: no equal sides

• Isosceles: two equal sides

• Equilateral: three equal sides

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32. Draw a sketch of a trapezium.
Answer: [Visual description] A quadrilateral with one pair of parallel sides. Often drawn with horizontal parallel lines, the other two sides non-parallel.

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33. A triangle has one line of symmetry and no rotational symmetry. What type of triangle is it?
Answer: Isosceles triangle
Explanation: An isosceles triangle has exactly one line of symmetry (through the vertex angle to the midpoint of the base) and rotational symmetry of order 1 (none).

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34. True or False: A rhombus is a regular polygon.
Answer: False
Explanation: A regular polygon must have all sides equal AND all angles equal. A rhombus has all sides equal but not necessarily all angles equal (unless it's a square).

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35. What is the size of each angle in an equilateral triangle?
Answer: 60°
Explanation: All angles equal in equilateral triangle → 180° ÷ 3 = 60°.

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36. A quadrilateral has rotational symmetry of order 4. What could it be?
Answer: Square
Explanation: Among quadrilaterals, only a square has rotational symmetry of order 4 (90° rotations). A rhombus has order 2.

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37. How many pairs of equal sides does an isosceles triangle have?
Answer: 1 pair
Explanation: Exactly two sides are equal in an isosceles triangle, forming one pair of equal sides.

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38. What is the sum of the angles in any quadrilateral?
Answer: 360°
Explanation: Formula: $(n-2)\times 180\mathrm{°}$ with n=4 → $2\times 180\mathrm{°}=360\mathrm{°}$.

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39. A shape has four lines of symmetry and rotational symmetry of order 4. What is it?
Answer: Square
Explanation: A square has 4 lines of symmetry (through opposite vertices and midpoints) and rotational symmetry of order 4.

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40. True or False: Every square is a rhombus.
Answer: True
Explanation: A square meets the definition of a rhombus (all sides equal) with the additional property of all angles being 90°.

Section C: Properties of 2D Shapes

41. In an isosceles triangle, the angle at the apex (top) is 40°. What is the size of each base angle?
Answer: 70°
Explanation: Sum of angles = 180°. Let each base angle = $x$. Then $40\mathrm{°}+x+x=180\mathrm{°}$ → $2x=140\mathrm{°}$ → $x=70\mathrm{°}$.

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42. A rectangle has a length of 8cm and a width of 5cm. What is the perimeter?
Answer: 26 cm
Explanation: Perimeter of rectangle = $2\times (\text{length}+\text{width})=2\times (8+5)=2\times 13=26$ cm.

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43. A square has a perimeter of 36cm. What is its area?
Answer: 81 cm²
Explanation: Perimeter = $4\times \text{side}$. Side = $36÷4=9$ cm. Area = side² = $9\times 9=81$ cm².

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44. A parallelogram has an area of 20 cm² and a base of 5 cm. What is its height?
Answer: 4 cm
Explanation: Area of parallelogram = base × height. So $20=5\times h$ → $h=20÷5=4$ cm.

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45. A triangle is drawn on a centimetre grid. Its vertices are at (1,1), (1,5), and (4,1). What is its area?
Answer: 6 cm²
Explanation: This is a right-angled triangle with:

• Base along x-axis from (1,1) to (4,1) → length = 3 cm

• Height along y-axis from (1,1) to (1,5) → length = 4 cm
  Area = $\text{½}\times \text{base}\times \text{height}=\text{½}\times 3\times 4=6$ cm².

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46. What is the name given to the longest side of a right-angled triangle?
Answer: Hypotenuse
Explanation: In a right-angled triangle, the side opposite the right angle is the hypotenuse, and it is always the longest side (by Pythagoras).

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47. If two angles in a triangle are 45° and 55°, what is the third angle and what type of triangle is it?
Answer: 80°, acute-angled triangle
Explanation: Third angle = $180\mathrm{°}-(45\mathrm{°}+55\mathrm{°})=80\mathrm{°}$. All angles < 90°, so acute-angled.

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48. A quadrilateral has exactly two lines of symmetry. It is not a rectangle. What could it be?
Answer: Rhombus
Explanation: A rectangle has 2 lines of symmetry, but if "not a rectangle," another possibility is a rhombus (lines through opposite vertices).

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49. How many sides does a heptagon have?
Answer: 7
Explanation: Greek prefixes: hepta- = 7.

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50. True or False: A trapezium can have a right angle.
Answer: True
Explanation: A right-angled trapezium has two right angles adjacent to each other on one of the parallel sides.

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51. A regular polygon has an interior angle of 135°. How many sides does it have?
Answer: 8 sides (octagon)
Explanation: If interior = 135°, exterior = 180° - 135° = 45°. Sides = $360\mathrm{°}÷45\mathrm{°}=8$.

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52. What is the exterior angle of a regular nonagon?
Answer: 40°
Explanation: Nonagon = 9 sides. Exterior angle = $360\mathrm{°}÷9=40\mathrm{°}$.

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53. A triangle has sides of length 5 cm, 5 cm, and 8 cm. What type of triangle is it?
Answer: Isosceles triangle
Explanation: Two sides equal (5 cm) → isosceles.

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54. A triangle has sides of length 3 cm, 4 cm, and 5 cm. What type of triangle is it?
Answer: Right-angled triangle
Explanation: $3^2+4^2=9+16=25=5^2$, so it satisfies Pythagoras' theorem → right-angled.

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55. A quadrilateral has all sides equal and one angle of 90°. What is its name?
Answer: Square
Explanation: All sides equal → rhombus. One angle 90° → all angles 90° (because adjacent angles supplementary, opposite angles equal) → square.

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56. A quadrilateral has opposite angles equal and all sides equal, but it is not a square. What is it?
Answer: Rhombus
Explanation: All sides equal = rhombus. If not a square, then angles are not 90°.

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57. How many lines of symmetry does a regular hexagon have?
Answer: 6
Explanation: A regular hexagon has 6 lines of symmetry (through opposite vertices and through midpoints of opposite sides).

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58. What is the order of rotational symmetry of an equilateral triangle?
Answer: 3
Explanation: Fits onto itself 3 times in a 360° rotation (at 120°, 240°, 360°).

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59. True or False: A circle has infinite lines of symmetry.
Answer: True
Explanation: Any line through the center of a circle is a line of symmetry → infinite such lines.

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60. A shape has rotational symmetry of order 2 and no line symmetry. What could it be?
Answer: Parallelogram (non-rectangle, non-rhombus)
Explanation: Example: a slanted parallelogram (not rectangle, not rhombus) has order 2 rotational symmetry but no lines of symmetry.

61. A triangle has an area of 15 cm² and a base of 6 cm. What is its height?
Answer: 5 cm
Explanation: Area of triangle = $\text{½}\times \text{base}\times \text{height}$.
$15=\text{½}\times 6\times h$
$15=3h$
$h=5$ cm.

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62. A square has an area of 49 cm². What is its perimeter?
Answer: 28 cm
Explanation: Area = side² = 49 → side = √49 = 7 cm.
Perimeter = $4\times \text{side}=4\times 7=28$ cm.

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63. A rectangle has a perimeter of 24 cm and a length of 8 cm. What is its width?
Answer: 4 cm
Explanation: Perimeter = $2(\text{length}+\text{width})$.
$24=2(8+w)$
$12=8+w$
$w=4$ cm.

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64. A parallelogram has a base of 10 cm and a height of 3 cm. What is its area?
Answer: 30 cm²
Explanation: Area of parallelogram = base × height = $10\times 3=30$ cm².

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65. A trapezium has parallel sides of 6 cm and 10 cm, and a height of 4 cm. What is its area?
Answer: 32 cm²
Explanation: Area of trapezium = $\text{½}\times (\text{sum of parallel sides})\times \text{height}$
= $\text{½}\times (6+10)\times 4$
= $\text{½}\times 16\times 4$
= $8\times 4=32$ cm².

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66. What is the name of a triangle with all angles less than 90°?
Answer: Acute-angled triangle

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67. What is the name of a triangle with one angle greater than 90°?
Answer: Obtuse-angled triangle

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68. True or False: A rhombus has diagonals that bisect each other at right angles.
Answer: True
Explanation: This is a key property of a rhombus (and also of a square, which is a special rhombus).

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69. How many vertices does a pentagon have?
Answer: 5

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70. What is the name of a quadrilateral where diagonals are equal and bisect each other at right angles?
Answer: Square
Explanation: Only a square has all these properties among quadrilaterals.

• Diagonals equal ✓ (rectangle also has this, but doesn't bisect at right angles)

• Diagonals bisect each other ✓ (all parallelograms have this)

• Diagonals bisect at right angles ✓ (rhombus has this, but diagonals aren't equal)
  Only a square satisfies all three.

Section D: Angle Rules (First 15 of 30 questions)

71. Two angles on a straight line are 125° and *x*. Find *x*.
Answer: 55°
Explanation: Angles on a straight line sum to 180°.
$125\mathrm{°}+x=180\mathrm{°}$
$x=180\mathrm{°}-125\mathrm{°}=55\mathrm{°}$

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72. Three angles around a point are 100°, 150° and *y*. Find *y*.
Answer: 110°
Explanation: Angles around a point sum to 360°.
$100\mathrm{°}+150\mathrm{°}+y=360\mathrm{°}$
$250\mathrm{°}+y=360\mathrm{°}$
$y=360\mathrm{°}-250\mathrm{°}=110\mathrm{°}$

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73. In the diagram, two straight lines cross. One angle is 40°. What are the sizes of the other three angles?
Answer: 40°, 140°, 140°
Explanation: Vertically opposite angles are equal → one opposite angle is 40°. Adjacent angles on a straight line are supplementary → $180\mathrm{°}-40\mathrm{°}=140\mathrm{°}$. So the four angles are: 40°, 140°, 40°, 140°.

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74. In an isosceles triangle, the vertex angle is 50°. What is the size of each base angle?
Answer: 65°
Explanation: Sum of angles = 180°. Let each base angle = $b$.
$50\mathrm{°}+b+b=180\mathrm{°}$
$50\mathrm{°}+2b=180\mathrm{°}$
$2b=130\mathrm{°}$
$b=65\mathrm{°}$

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75. A quadrilateral has angles of 80°, 95°, and 110°. What is the fourth angle?
Answer: 75°
Explanation: Sum of angles in quadrilateral = 360°.
$80\mathrm{°}+95\mathrm{°}+110\mathrm{°}+x=360\mathrm{°}$
$285\mathrm{°}+x=360\mathrm{°}$
$x=360\mathrm{°}-285\mathrm{°}=75\mathrm{°}$

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76. Find the size of angle *a* in a triangle with angles 60° and 70°.
Answer: 50°
Explanation: Triangle sum = 180°.
$a=180\mathrm{°}-(60\mathrm{°}+70\mathrm{°})=180\mathrm{°}-130\mathrm{°}=50\mathrm{°}$

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77. Angles *p* and *q* are vertically opposite. If *p* is 110°, what is *q*?
Answer: 110°
Explanation: Vertically opposite angles are equal.

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78. In a right-angled triangle, one acute angle is twice the other. What are the sizes of the angles?
Answer: 30°, 60°, 90°
Explanation: Let smaller acute angle = $x$, then larger acute = $2x$.
Right angle = 90°.
$x+2x+90\mathrm{°}=180\mathrm{°}$
$3x=90\mathrm{°}$
$x=30\mathrm{°}$, so angles are 30°, 60°, 90°.

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79. A straight line has three angles on it, *x*, 2*x*, and 90°. Find the value of *x*.
Answer: 30°
Explanation: Angles on a straight line sum to 180°.
$x+2x+90\mathrm{°}=180\mathrm{°}$
$3x=90\mathrm{°}$
$x=30\mathrm{°}$

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80. In a parallelogram, one angle is 110°. What are the sizes of the other three angles?
Answer: 110°, 70°, 70°
Explanation: Opposite angles equal → another 110°. Adjacent angles supplementary → $180\mathrm{°}-110\mathrm{°}=70\mathrm{°}$. So angles: 110°, 70°, 110°, 70°.

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81. The angles of a triangle are in the ratio 2:3:4. Find the size of the largest angle.
Answer: 80°
Explanation: Let angles = $2x,3x,4x$.
Sum: $2x+3x+4x=180\mathrm{°}$
$9x=180\mathrm{°}$
$x=20\mathrm{°}$
Largest = $4x=4\times 20\mathrm{°}=80\mathrm{°}$

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82. In a rhombus, one angle is 65°. What is the size of the angle adjacent to it?
Answer: 115°
Explanation: Adjacent angles in a rhombus (parallelogram property) are supplementary.
$180\mathrm{°}-65\mathrm{°}=115\mathrm{°}$

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83. Angles *a* and *b* are on a straight line. Angle *a* is 3 times angle *b*. Find angle *b*.
Answer: 45°
Explanation: $a+b=180\mathrm{°}$ and $a=3b$
$3b+b=180\mathrm{°}$
$4b=180\mathrm{°}$
$b=45\mathrm{°}$

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84. Four angles around a point are 2*x*, 3*x*, 4*x*, and 5*x*. Find the value of *x*.
Answer: $x={\frac{180}{7}}^{\circ }$ or ≈ 25.71°
Explanation: Sum around a point = 360°.
$2x+3x+4x+5x=360\mathrm{°}$
$14x=360\mathrm{°}$
$x=\frac{360\mathrm{°}}{14}=\frac{180\mathrm{°}}{7}$

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85. In a pentagon, four of the angles are 100°, 110°, 120°, and 130°. What is the fifth angle?
Answer: 80°
Explanation: Sum of interior angles of pentagon = $(5-2)\times 180\mathrm{°}=540\mathrm{°}$.
Given angles sum: $100+110+120+130=460\mathrm{°}$.
Fifth angle = $540\mathrm{°}-460\mathrm{°}=80\mathrm{°}$

Section D: Angle Rules (Questions 86–100)

86. An isosceles triangle has a base angle of 40°. What is the vertex angle?
Answer: 100°
Explanation: Base angles in an isosceles triangle are equal → both base angles = 40°.
Vertex angle = $180\mathrm{°}-(40\mathrm{°}+40\mathrm{°})=180\mathrm{°}-80\mathrm{°}=100\mathrm{°}$.

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87. Two angles in a triangle are 35° and 45°. What is the third angle?
Answer: 100°
Explanation: $180\mathrm{°}-(35\mathrm{°}+45\mathrm{°})=180\mathrm{°}-80\mathrm{°}=100\mathrm{°}$.

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88. In a quadrilateral, three angles are equal and the fourth is 90°. What is the size of each of the equal angles?
Answer: 90°
Explanation: Let each equal angle = $x$.
Sum: $3x+90\mathrm{°}=360\mathrm{°}$
$3x=270\mathrm{°}$
$x=90\mathrm{°}$.

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89. Angles *c* and *d* are complementary. Angle *c* is 15° more than angle *d*. Find angle *c*.
Answer: 52.5°
Explanation: Complementary → $c+d=90\mathrm{°}$
Given: $c=d+15\mathrm{°}$
Substitute: $(d+15\mathrm{°})+d=90\mathrm{°}$
$2d+15\mathrm{°}=90\mathrm{°}$
$2d=75\mathrm{°}$
$d=37.5\mathrm{°}$
$c=37.5\mathrm{°}+15\mathrm{°}=52.5\mathrm{°}$.

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90. The exterior angle of a triangle is 120° and one of its interior opposite angles is 50°. What is the other interior opposite angle?
Answer: 70°
Explanation: Exterior angle = sum of the two opposite interior angles.
$120\mathrm{°}=50\mathrm{°}+x$
$x=120\mathrm{°}-50\mathrm{°}=70\mathrm{°}$.

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91. In a trapezium with one pair of parallel sides, one angle is 85°. What is the angle on the same side of the transversal?
Answer: 95°
Explanation: In a trapezium, angles on the same side of the transversal (between a parallel line and the non-parallel side) are supplementary if the lines are parallel.
$180\mathrm{°}-85\mathrm{°}=95\mathrm{°}$.

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92. A triangle has angles of (x+10)°, (2x-20)°, and 60°. Find the value of x.
Answer: $x=\frac{130}{3}$ ≈ 43.33°
Explanation: Sum: $(x+10)+(2x-20)+60=180$
$3x+50=180$
$3x=130$
$x=\frac{130}{3}$.

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93. A quadrilateral has angles of x, 2x, 3x, and 4x. Find the value of x.
Answer: 36°
Explanation: Sum: $x+2x+3x+4x=10x=360\mathrm{°}$
$x=36\mathrm{°}$.

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94. In a regular hexagon, what is the size of each interior angle?
Answer: 120°
Explanation: Sum of interior angles = $(6-2)\times 180\mathrm{°}=720\mathrm{°}$.
Each interior angle = $720\mathrm{°}÷6=120\mathrm{°}$.

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95. The angles of a triangle are (2y)°, (3y)°, and (4y)°. Find the value of y.
Answer: 20°
Explanation: Sum: $2y+3y+4y=9y=180\mathrm{°}$
$y=20\mathrm{°}$.

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96. On a straight line, angles are 2a, 3a, and 4a. Find the smallest angle.
Answer: 40°
Explanation: Sum: $2a+3a+4a=9a=180\mathrm{°}$
$a=20\mathrm{°}$.
Smallest angle = $2a=2\times 20\mathrm{°}=40\mathrm{°}$.

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97. Around a point, angles are a, 2a, 3a, 4a, and 5a. Find the largest angle.
Answer: 120°
Explanation: Sum: $a+2a+3a+4a+5a=15a=360\mathrm{°}$
$a=24\mathrm{°}$.
Largest = $5a=5\times 24\mathrm{°}=120\mathrm{°}$.

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98. In an isosceles triangle, the vertex angle is 4 times a base angle. Find the vertex angle.
Answer: 120°
Explanation: Let base angle = $b$, vertex = $4b$.
Sum: $b+b+4b=180\mathrm{°}$
$6b=180\mathrm{°}$
$b=30\mathrm{°}$.
Vertex = $4\times 30\mathrm{°}=120\mathrm{°}$.

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99. Two vertically opposite angles are (3x+10)° and (5x-20)°. Find the value of x.
Answer: 15
Explanation: Vertically opposite angles are equal:
$3x+10=5x-20$
$10+20=5x-3x$
$30=2x$
$x=15$.

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100. In a right-angled isosceles triangle, what are the sizes of the two acute angles?
Answer: 45° each
Explanation: Right angle = 90°, remaining two acute angles are equal and sum to 90°. Each = $90\mathrm{°}÷2=45\mathrm{°}$.

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -2

 

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -2

Section E: Properties of 3D Shapes (30 Questions)

101. How many faces does a cube have?

102. How many edges does a cuboid have?

103. How many vertices does a square-based pyramid have?

104. What is the name of a 3D shape with a circular base and a vertex?

105. How many edges does a triangular prism have?

106. What 2D shape are the faces of a tetrahedron?

107. A cylinder has how many flat faces?

108. What is the name of a 3D shape with 6 rectangular faces?

109. A cone has how many vertices?

110. How many faces does a hexagonal prism have?

111. If a cube has a side length of 4cm, what is its volume?

112. What is the surface area of a cube with side length 3cm?

113. A cuboid is 5cm long, 4cm wide, and 3cm high. What is its volume?

114. How many pairs of parallel faces does a cuboid have?

115. True or False: A sphere has any edges or vertices.

116. What is the name of the 3D shape that is like a ball?

117. A triangular prism has how many rectangular faces?

118. What is the cross-section of a cylinder?

119. How many more vertices does a cube have than a square-based pyramid?

120. A prism has a constant cross-section. What is the cross-section of a pentagonal prism?

121. If you cut a cube parallel to one of its faces, what shape is the cross-section?

122. What 3D shape can be made by stacking many congruent circles?

123. A cube has a volume of 64 cm³. What is the length of one edge?

124. A cuboid has a volume of 60 cm³, a length of 5cm, and a width of 4cm. What is its height?

125. How many edges meet at each vertex of a cube?

126. What is the name of a 3D shape with all faces being equilateral triangles?

127. A cylinder has a radius of 3cm and a height of 10cm. What is its volume? (Use π=3.14)

128. True or False: A cone has two faces.

129. How many lateral faces does a square-based pyramid have?

130. What is the name for the point where edges of a 3D shape meet?

Section F: Fictional "Previous Year Paper" (50 Questions)

This section mixes all topics in a simulated exam paper format.

131. Calculate 345 + 678.

132. What is 7/8 of 400?

133. Write 0.75 as a fraction in its simplest form.

134. What is the perimeter of a rectangle 12cm by 8cm?

135. A car travels 60km in 45 minutes. What is its speed in km/h?

136. Simplify the ratio 24:18.

137. What is the mean of 5, 7, 9, 11, 13?

138. A book costs £6.40. How much change from £10?

139. What is the next number in the sequence: 5, 9, 13, 17, ...?

140. Find 15% of £80.

141. An angle is 145°. What type of angle is it?

142. What is the sum of the interior angles of a triangle?

143. How many sides does a decagon have?

144. A triangle has sides 6cm, 8cm, 10cm. What type of triangle is it?

145. What is the name of a quadrilateral with one pair of parallel sides?

146. How many lines of symmetry does a rectangle have?

147. A cube has how many faces?

148. A regular polygon has an exterior angle of 36°. How many sides does it have?

149. In a pie chart, an angle of 90° represents what fraction of the total?

150. A bag has 3 red and 5 blue marbles. What is the probability of picking a red one?

151. Solve 3x + 7 = 22.

152. What is the area of a triangle with base 10cm and height 6cm?

153. Write 4.5 x 10^4 as an ordinary number.

154. A map scale is 1:50,000. What is 4cm on the map in real life (km)?

155. Decrease £120 by 15%.

156. Two angles are supplementary. One is 85°. What is the other?

157. What is the order of rotational symmetry of a regular hexagon?

158. A cuboid is 6cm x 4cm x 2cm. What is its volume?

159. What is the square root of 144?

160. What is the value of 5³?

161. A train leaves at 14:25 and arrives at 17:10. How long is the journey?

162. Share £60 in the ratio 2:3.

163. Estimate 398 x 51.

164. Round 7.846 to 2 decimal places.

165. What is the reciprocal of 5?

166. Find the mode of 3, 5, 5, 6, 7, 5, 8.

167. A dice is rolled. What is the probability of getting an even number?

168. A regular polygon has interior angles of 150°. How many sides does it have?

169. Angles in a quadrilateral are 90°, 100°, 110° and *x*. Find *x*.

170. A square has area 36cm². What is its perimeter?

171. A triangle has angles of 2x, 3x, and 4x. Find the value of x.

172. How many edges does a triangular-based pyramid have?

173. What is the name of a 3D shape with a circular base and a curved surface that tapers to a point?

174. A coat costs £80. In a sale, it is reduced by 20%. What is the sale price?

175. If a = 5 and b = 3, what is the value of 2a² - b?

176. Solve 2(y - 3) = 16.

177. Find the median of 8, 3, 5, 1, 9.

178. A recipe for 4 needs 200g flour. How much for 10?

179. What is the range of 12, 15, 18, 12, 20?

180. A pack of 6 drinks costs £3.60. What is the cost per drink?

Section G: Previous Year GL Assessment Styles (50 Questions)

This final section focuses purely on multi-choice, GL-style geometry questions.

181. Which angle is obtuse? A) 45° B) 90° C) 100° D) 180°

182. What is the size of one interior angle of an equilateral triangle? A) 30° B) 60° C) 90° D) 120°

183. How many sides does a nonagon have? A) 7 B) 8 C) 9 D) 10

184. Which shape has exactly one line of symmetry? A) Square B) Equilateral Triangle C) Rectangle D) Isosceles Triangle

185. What is the sum of the exterior angles of any polygon? A) 180° B) 360° C) 90° D) Depends on the number of sides

186. A cube has: A) 6 faces, 12 edges, 8 vertices B) 8 faces, 12 edges, 6 vertices C) 6 faces, 8 edges, 12 vertices D) 4 faces, 12 edges, 8 vertices

187. Which of these is a regular polygon? A) Rectangle B) Rhombus C) Square D) Isosceles Triangle

188. Two angles in a triangle are 40° and 50°. The triangle is: A) Obtuse-angled B) Acute-angled C) Right-angled D) Equilateral

189. A quadrilateral with all sides equal and all angles 90° is a: A) Rhombus B) Parallelogram C) Square D) Kite

190. The order of rotational symmetry of a parallelogram is: A) 0 B) 1 C) 2 D) 4

191. The angle on a straight line next to a 115° angle is: A) 65° B) 75° C) 245° D) 295°

192. A triangular prism has: A) 5 faces B) 6 faces C) 8 faces D) 9 faces

193. The interior angles of a hexagon add up to: A) 540° B) 720° C) 900° D) 1080°

194. Which shape is not a quadrilateral? A) Trapezium B) Pentagon C) Kite D) Parallelogram

195. A square-based pyramid has: A) 5 faces B) 6 faces C) 8 faces D) 10 faces

196. The supplement of 70° is: A) 20° B) 110° C) 290° D) 250°

197. A shape with rotational symmetry of order 1 has: A) No symmetry B) One line of symmetry C) Two lines of symmetry D) Infinite symmetry

198. A cuboid has a volume of 48 cm³. Its length is 6cm and width is 2cm. What is its height? A) 4cm B) 6cm C) 8cm D) 12cm

199. The angles in an isosceles triangle are 40°, 40° and x°. The value of x is: A) 40 B) 80 C) 100 D) 140

200. A regular polygon has 15 sides. The sum of its interior angles is: A) 2340° B) 2160° C) 1980° D) 1800°

201. Which net will make a cube? (Image description: Four options showing different arrangements of 6 squares)

202. The area of a triangle is 24 cm². Its base is 8cm. What is its height? A) 3cm B) 4cm C) 6cm D) 8cm

203. A kite has one pair of opposite angles equal. If one is 80°, the other is: A) 80° B) 100° C) 160° D) Cannot tell

204. The number of lines of symmetry in a regular octagon is: A) 4 B) 6 C) 8 D) 10

205. A cylinder has: A) 0 vertices B) 1 vertex C) 2 vertices D) 4 vertices

206. The exterior angle of a regular polygon is 18°. How many sides does it have? A) 10 B) 18 C) 20 D) 36

207. In a rhombus, if one angle is 50°, the angle opposite to it is: A) 40° B) 50° C) 130° D) 150°

208. The probability of rolling a 3 on a fair dice is: A) 1/2 B) 1/3 C) 1/6 D) 3/6

209. 2/5 of a number is 16. What is the number? A) 20 B) 32 C) 40 D) 64

210. The value of 7² + 4³ is: A) 33 B) 65 C) 113 D) 305

211. The mean of 5 numbers is 8. Four of the numbers are 6, 9, 7, 10. What is the fifth number? A) 6 B) 7 C) 8 D) 9

212. A TV costs £400 plus 20% VAT. What is the total cost? A) £420 B) £480 C) £800 D) £4000

213. 2.5 hours is the same as: A) 150 mins B) 160 mins C) 180 mins D) 250 mins

214. The perimeter of a square is 28cm. Its area is: A) 49 cm² B) 56 cm² C) 196 cm² D) 784 cm²

215. In a class of 30, 18 are girls. What fraction are boys? A) 3/5 B) 2/5 C) 3/4 D) 1/2

216. The next number in the sequence 1, 3, 6, 10, ... is: A) 13 B) 14 C) 15 D) 16

217. 0.08 written as a fraction is: A) 4/5 B) 2/25 C) 8/10 D) 1/8

218. A bus has 50 seats. 90% are full. How many seats are empty? A) 5 B) 10 C) 40 D) 45

219. Which is the smallest? A) 0.7 B) 0.699 C) 0.71 D) 0.709

220. What is 30% of £250? A) £75 B) £85 C) £95 D) £750

221. A box holds 12 pencils. How many boxes for 300 pencils? A) 25 B) 28 C) 30 D) 36

222. The time 20:35 in 12-hour clock is: A) 8:35 am B) 8:35 pm C) 10:35 am D) 10:35 pm

223. A triangle with vertices (1,1), (1,4), (5,1) is: A) Scalene B) Isosceles C) Equilateral D) Right-angled

224. A square of side 5cm has the same area as a rectangle 10cm long. How wide is the rectangle? A) 2.5cm B) 5cm C) 10cm D) 15cm

225. A car uses 40 litres for 500km. How much for 150km? A) 10 litres B) 12 litres C) 15 litres D) 20 litres

226. Which is the best estimate for 59 x 61? A) 3000 B) 3500 C) 3600 D) 4000

227. Simplify 4a + 3b - a + 2b. A) 3a + 5b B) 4a + 5b C) 5a + 3b D) 7a + 5b

228. If 4x - 7 = 25, then x is: A) 4.5 B) 8 C) 9 D) 10

229. The range of 2, 5, 8, 3, 5 is: A) 3 B) 5 C) 6 D) 8

230. A dice is rolled twice. The probability of getting two sixes is: A) 1/6 B) 1/12 C) 1/18 D) 1/36

ANSWER KEY WITH EXPLANATION

Section E: 3D Shapes & Properties

1. How many faces does a cube have?
A cube has 6 faces (all squares).
Answer: 6

2. How many edges does a cuboid have?
A cuboid has 12 edges.
Answer: 12

3. How many vertices does a square-based pyramid have?
Square base (4 vertices) + apex (1) = 5 vertices.
Answer: 5

4. What is the name of a 3D shape with a circular base and a vertex?
Cone.
Answer: Cone

5. How many edges does a triangular prism have?
Triangular prism: 2 triangular faces, 3 rectangular faces → 9 edges.
Check: triangles have 3 edges each but prism has side edges: total edges = 3 × 3 = 9.
Answer: 9

6. What 2D shape are the faces of a tetrahedron?
All faces are equilateral triangles.
Answer: Equilateral triangles

7. A cylinder has how many flat faces?
Two circular flat faces (top and bottom) = 2 flat faces.
Answer: 2

8. What is the name of a 3D shape with 6 rectangular faces?
Cuboid (or rectangular prism).
Answer: Cuboid

9. A cone has how many vertices?
A cone has 1 vertex (apex).
Answer: 1

10. How many faces does a hexagonal prism have?
Hexagonal prism: 2 hexagonal faces + 6 rectangular faces = 8 faces.
Answer: 8

11. If a cube has a side length of 4cm, what is its volume?
Volume = side³ = 4³ = 64 cm³.
Answer: 64 cm³

12. What is the surface area of a cube with side length 3cm?
Surface area = 6 × side² = 6 × 9 = 54 cm².
Answer: 54 cm²

13. A cuboid is 5cm long, 4cm wide, and 3cm high. What is its volume?
Volume = length × width × height = 5 × 4 × 3 = 60 cm³.
Answer: 60 cm³

14. How many pairs of parallel faces does a cuboid have?
A cuboid has 3 pairs of parallel faces.
Answer: 3

15. True or False: A sphere has any edges or vertices.
False — a sphere has no edges and no vertices.
Answer: False

16. What is the name of the 3D shape that is like a ball?
Sphere.
Answer: Sphere

17. A triangular prism has how many rectangular faces?
Triangular prism: 3 rectangular faces (if right prism) + 2 triangular faces.
Answer: 3

18. What is the cross-section of a cylinder?
A cross-section parallel to base is a circle.
Answer: Circle

19. How many more vertices does a cube have than a square-based pyramid?
Cube vertices = 8, pyramid vertices = 5. Difference = 3 more.
Answer: 3

20. A prism has a constant cross-section. What is the cross-section of a pentagonal prism?
Pentagon.
Answer: Pentagon

21. If you cut a cube parallel to one of its faces, what shape is the cross-section?
Square.
Answer: Square

22. What 3D shape can be made by stacking many congruent circles?
Cylinder.
Answer: Cylinder

23. A cube has a volume of 64 cm³. What is the length of one edge?
Edge length = cube root of 64 = 4 cm.
Answer: 4 cm

24. A cuboid has a volume of 60 cm³, a length of 5cm, and a width of 4cm. What is its height?
Height = Volume ÷ (length × width) = 60 ÷ (5 × 4) = 60 ÷ 20 = 3 cm.
Answer: 3 cm

25. How many edges meet at each vertex of a cube?
3 edges meet at each vertex of a cube.
Answer: 3

26. What is the name of a 3D shape with all faces being equilateral triangles?
Tetrahedron (if 4 faces) or possibly octahedron (8 faces) but simplest: tetrahedron.
Given: all faces equilateral triangles → tetrahedron has 4 such triangles.
Answer: Tetrahedron

27. A cylinder has a radius of 3cm and a height of 10cm. What is its volume? (Use π=3.14)
Volume = πr²h = 3.14 × 9 × 10 = 282.6 cm³.
Answer: 282.6 cm³

28. True or False: A cone has two faces.
True — one curved face + one circular flat face = 2 faces.
Answer: True

29. How many lateral faces does a square-based pyramid have?
Lateral faces = faces excluding base = 4 triangular faces.
Answer: 4

30. What is the name for the point where edges of a 3D shape meet?
Vertex (plural vertices).
Answer: Vertex

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Section F: Fictional "Previous Year Paper"

31. 345 + 678 = 1023
    Answer: 1023

32. 7/8 of 400 = 350
    Answer: 350

33. 0.75 = 3/4
    Answer: 3/4

34. Perimeter of rectangle 12cm by 8cm = 2×(12+8) = 40 cm
    Answer: 40 cm

35. Speed: 45 mins = 0.75 hours → speed = 60 km ÷ 0.75 h = 80 km/h
    Answer: 80 km/h

36. Simplify 24:18 = 4:3
    Answer: 4:3

37. Mean of 5,7,9,11,13 = (5+7+9+11+13)/5 = 45/5 = 9
    Answer: 9

38. Change from £10 for £6.40 = £3.60
    Answer: £3.60

39. Next in sequence 5,9,13,17 → +4 → 21
    Answer: 21

40. 15% of £80 = £12
    Answer: £12

41. 145° = Obtuse angle (between 90° and 180°)
    Answer: Obtuse

42. Sum of interior angles of a triangle = 180°
    Answer: 180°

43. Decagon sides = 10
    Answer: 10

44. Sides 6,8,10 → right-angled (6²+8²=10²)
    Answer: Right-angled

45. Quadrilateral with one pair of parallel sides = Trapezium
    Answer: Trapezium

46. Lines of symmetry in a rectangle = 2
    Answer: 2

47. Cube faces = 6
    Answer: 6

48. Exterior angle 36° → sides = 360/36 = 10
    Answer: 10

49. 90° in pie chart = 1/4 of total
    Answer: 1/4

50. Probability red = 3/(3+5) = 3/8
    Answer: 3/8

51. 3x + 7 = 22 → 3x=15 → x=5
    Answer: 5

52. Area of triangle = ½×10×6 = 30 cm²
    Answer: 30 cm²

53. 4.5×10⁴ = 45,000
    Answer: 45,000

54. Scale 1:50,000 → 4 cm = 4×50,000 cm = 200,000 cm = 2 km
    Answer: 2 km

55. Decrease £120 by 15%: 15% of 120 = 18 → 120−18 = 102
    Answer: £102

56. Supplementary to 85° = 95°
    Answer: 95°

57. Rotational symmetry of regular hexagon = order 6
    Answer: 6

58. Cuboid volume 6×4×2 = 48 cm³
    Answer: 48 cm³

59. √144 = 12
    Answer: 12

60. 5³ = 125
    Answer: 125

61. Journey 14:25 to 17:10 = 2h45m = 2.75h or 165 mins
    Answer: 2h45m or 165 mins

62. Share £60 in 2:3 → 2/5×60=£24, 3/5×60=£36
    Answer: £24 and £36

63. Estimate 398×51 ≈ 400×50 = 20,000
    Answer: 20,000

64. 7.846 to 2 d.p. = 7.85
    Answer: 7.85

65. Reciprocal of 5 = 1/5
    Answer: 1/5

66. Mode of 3,5,5,6,7,5,8 = 5
    Answer: 5

67. Probability even on dice = 3/6 = 1/2
    Answer: 1/2

68. Interior 150° → exterior 30° → sides = 360/30 = 12
    Answer: 12

69. Quadrilateral: 90+100+110+x=360 → x=60°
    Answer: 60°

70. Area 36cm² → side = 6cm → perimeter = 24cm
    Answer: 24 cm

71. 2x+3x+4x=180 → 9x=180 → x=20°
    Answer: 20

72. Triangular-based pyramid edges = 6
    Answer: 6

73. Circular base, tapers to point = Cone
    Answer: Cone

74. £80 reduced by 20% = 80−16=£64
    Answer: £64

75. a=5, b=3 → 2a²−b = 2×25−3=50−3=47
    Answer: 47

76. 2(y−3)=16 → y−3=8 → y=11
    Answer: 11

77. Median of 1,3,5,8,9 = 5
    Answer: 5

78. Recipe: for 10 people → 200×(10/4)=500g flour
    Answer: 500 g

79. Range of 12,15,18,12,20 = 20−12=8
    Answer: 8

80. Cost per drink = £3.60 ÷ 6 = £0.60
    Answer: £0.60

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Section G: Multi-Choice GL Style

81. Obtuse angle: C) 100° (between 90° and 180°)
    Answer: C

82. Equilateral triangle interior angle: B) 60°
    Answer: B

83. Nonagon sides: C) 9
    Answer: C

84. Exactly one line of symmetry: D) Isosceles Triangle
    Answer: D

85. Sum exterior angles: B) 360° (always)
    Answer: B

86. Cube facts: A) 6 faces, 12 edges, 8 vertices
    Answer: A

87. Regular polygon: C) Square
    Answer: C

88. Triangle with 40°,50° → third 90°: C) Right-angled
    Answer: C

89. All sides equal, all angles 90°: C) Square
    Answer: C

90. Rotational symmetry of parallelogram: C) 2
    Answer: C

91. On straight line next to 115°: A) 65°
    Answer: A

92. Triangular prism faces: B) 6 faces (5 faces? No, it’s 5 actually? Wait: 2 triangles + 3 rectangles = 5 faces total? Check: triangular prism has 5 faces. But GL often says 5. Given options: A)5 B)6 C)8 D)9 → answer is A) 5 faces.)
    Actually: Standard triangular prism has 5 faces. But some count bases differently — but mathematically: 2 triangular + 3 rectangular = 5 faces.
    Answer: A) 5 faces

93. Hexagon interior sum: B) 720°
    Answer: B

94. Not quadrilateral: B) Pentagon
    Answer: B

95. Square-based pyramid faces: A) 5 faces
    Answer: A

96. Supplement of 70°: B) 110°
    Answer: B

97. Rotational symmetry order 1: A) No symmetry
    Answer: A

98. Cuboid volume 48, length 6, width 2: height = 48/(6×2)=4 → A) 4cm
    Answer: A

99. Isosceles triangle 40°,40°,x: C) 100°
    Answer: C

100. 15-sided polygon interior sum: A) 2340°
     Answer: A

101. Which net makes a cube? (No image, but typical answer is the one with 6 squares arranged in T or cross shape)
     Answer: (Cannot choose without image)

102. Triangle area 24, base 8: height = (2×24)/8=6 → C) 6cm
     Answer: C

103. Kite opposite angles equal: one 80°, other: A) 80°
     Answer: A

104. Lines of symmetry in regular octagon: C) 8
     Answer: C

105. Cylinder vertices: A) 0 vertices (curved surface, no vertices)
     Answer: A

106. Exterior angle 18° → sides = 360/18=20 → C) 20
     Answer: C

107. Rhombus opposite angle to 50°: B) 50°
     Answer: B

108. Probability of 3 on dice: C) 1/6
     Answer: C

109. 2/5 of number = 16 → number = 16×(5/2)=40 → C) 40
     Answer: C

110. 7² + 4³ = 49 + 64 = 113 → C) 113
     Answer: C

111. Mean of 5 numbers is 8, four are 6,9,7,10 total=32, fifth = 40−32=8 → C) 8
     Answer: C

112. £400 + 20% VAT = 400×1.2=480 → B) £480
     Answer: B

113. 2.5 hours = 150 mins → A) 150 mins
     Answer: A

114. Perimeter square 28cm → side=7cm → area=49cm² → A) 49 cm²
     Answer: A

115. Boys in class of 30 with 18 girls = 12 boys → fraction=12/30=2/5 → B) 2/5
     Answer: B

116. Sequence 1,3,6,10 → differences 2,3,4 → next 15 → C) 15
     Answer: C

117. 0.08 = 8/100=2/25 → B) 2/25
     Answer: B

118. Bus 90% full of 50 = 45 full, empty=5 → A) 5
     Answer: A

119. Smallest: B) 0.699
     Answer: B

120. 30% of £250 = £75 → A) £75
     Answer: A

121. 300 pencils ÷ 12 per box = 25 boxes → A) 25
     Answer: A

122. 20:35 in 12-hour = 8:35 pm → B) 8:35 pm
     Answer: B

123. Vertices (1,1),(1,4),(5,1) → right-angled at (1,1) → D) Right-angled
     Answer: D

124. Square side 5 area 25 → rectangle length 10 width=25/10=2.5 → A) 2.5cm
     Answer: A

125. Car 500km uses 40L → 1km=0.08L → 150km=12L → B) 12 litres
     Answer: B

126. Estimate 59×61 ≈ 60×60=3600 → C) 3600
     Answer: C

127. Simplify 4a+3b−a+2b = 3a+5b → A) 3a+5b
     Answer: A

128. 4x−7=25 → 4x=32 → x=8 → B) 8
     Answer: B

129. Range of 2,5,8,3,5 = 8−2=6 → C) 6
     Answer: C

130. Probability two sixes = (1/6)×(1/6)=1/36 → D) 1/36
     Answer: D