Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -5

 Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -5

Part 2: 100+ Practice Questions (GL Assessment Style)

Section 1: 2D Shapes & Polygons (30 Questions)

1. What is the name of a triangle with all sides different lengths?
   A) Equilateral B) Isosceles C) Scalene D) Right-angled

2. How many lines of symmetry does a regular hexagon have?
   A) 3 B) 4 C) 6 D) 8

3. A quadrilateral has exactly one pair of parallel sides. What is it called?
   A) Parallelogram B) Rhombus C) Trapezium D) Kite

4. What is the sum of interior angles in a pentagon?
   A) 360° B) 540° C) 720° D) 900°

5. A regular polygon has interior angles of 150°. How many sides does it have?
   A) 8 B) 10 C) 12 D) 15

6. Which quadrilateral always has diagonals that bisect each other at right angles?
   A) Rectangle B) Rhombus C) Parallelogram D) Trapezium

7. What is the size of each exterior angle of a regular nonagon?
   A) 30° B) 40° C) 45° D) 50°

8. True or False: A square is a special type of rhombus.

9. An isosceles triangle has a vertex angle of 80°. What is the size of each base angle?
   A) 40° B) 50° C) 60° D) 70°

10. How many diagonals does an octagon have?
    A) 16 B) 20 C) 24 D) 28

11. Which shape has rotational symmetry of order 2 but only one line of symmetry?
    A) Square B) Rectangle C) Rhombus D) Parallelogram

12. What type of triangle has angles 45°, 45°, and 90°?
    A) Scalene right-angled B) Isosceles right-angled C) Equilateral D) Obtuse

13. The interior angles of a quadrilateral are in the ratio 1:2:3:4. What is the size of the largest angle?
    A) 72° B) 96° C) 120° D) 144°

14. A regular polygon has an exterior angle of 24°. How many sides does it have?
    A) 12 B) 15 C) 18 D) 20

15. Which statement is true for all parallelograms?
    A) All angles are 90° B) All sides are equal C) Opposite sides are equal D) Diagonals are equal

16. What is the order of rotational symmetry of an equilateral triangle?
    A) 1 B) 2 C) 3 D) 4

17. A heptagon has how many sides?
    A) 5 B) 6 C) 7 D) 8

18. Three angles in a quadrilateral are 85°, 95°, and 110°. What is the fourth angle?
    A) 60° B) 70° C) 80° D) 90°

19. True or False: Every rectangle is a parallelogram.

20. A kite has one angle of 120° and another of 50°. What could the other two angles be?
    A) 120° and 50° B) 120° and 70° C) 95° and 95° D) 85° and 85°

21. What is the sum of exterior angles of any polygon?
    A) 90° × n B) 180° C) 360° D) 540°

22. A polygon has 10 sides. What is the sum of its interior angles?
    A) 1080° B) 1260° C) 1440° D) 1620°

23. Which shape has exactly two lines of symmetry?
    A) Square B) Rectangle C) Rhombus D) Kite

24. An equilateral triangle has perimeter 24cm. What is its area?
    A) 16√3 cm² B) 24 cm² C) 16 cm² D) 27.7 cm²

25. True or False: A trapezium can have two right angles.

26. What is the specific name for a quadrilateral with all sides equal and all angles 90°?

27. A regular polygon has interior angles of 162°. How many sides does it have?

28. The diagonals of which quadrilateral are always equal in length?
    A) Rhombus B) Square C) Rectangle D) Both B and C

29. What is the size of one interior angle of a regular dodecagon (12 sides)?

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

Section 2: 3D Shapes (20 Questions)

31. How many faces does a triangular prism have?
    A) 4 B) 5 C) 6 D) 8

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

33. What is the name of a 3D shape with 2 circular faces and 1 curved surface?
    A) Cone B) Cylinder C) Sphere D) Prism

34. How many vertices does a square-based pyramid have?
    A) 4 B) 5 C) 6 D) 8

35. A tetrahedron has how many triangular faces?
    A) 3 B) 4 C) 5 D) 6

36. Which net will make a cube?
    [Diagram showing different arrangements of 6 squares]

37. A cuboid has dimensions 5cm × 4cm × 3cm. What is its volume?
    A) 12 cm³ B) 48 cm³ C) 60 cm³ D) 120 cm³

38. How many edges does a hexagonal prism have?
    A) 12 B) 15 C) 18 D) 24

39. What shape are the faces of a dodecahedron?
    A) Squares B) Pentagons C) Hexagons D) Triangles

40. True or False: A cone has 2 faces and 1 edge.

41. If you slice a cube parallel to one face, what shape is the cross-section?
    A) Triangle B) Square C) Rectangle D) Hexagon

42. How many more edges does a cube have than a tetrahedron?
    A) 4 B) 6 C) 8 D) 12

43. A cylinder has radius 7cm and height 10cm. What is its volume? (Use π = 22/7)
    A) 1540 cm³ B) 154 cm³ C) 440 cm³ D) 15400 cm³

44. What is the surface area of a cube with side 5cm?
    A) 25 cm² B) 100 cm² C) 125 cm² D) 150 cm²

45. Which shape has Euler's formula F + V = E + 2?
    A) All polyhedra B) Only prisms C) Only pyramids D) Only cubes

46. How many rectangular faces does a triangular prism have?

47. What is the name of a prism with a pentagon as its cross-section?

48. A cube has volume 64 cm³. What is the length of one edge?
    A) 2cm B) 4cm C) 8cm D) 16cm

49. True or False: A sphere has faces, edges, and vertices.

50. Which 3D shape has exactly one vertex?
    A) Cube B) Cylinder C) Cone D) Sphere

Section 3: Angles & Angle Rules (30 Questions)

51. What type of angle is 125°?
    A) Acute B) Obtuse C) Reflex D) Right

52. Angles on a straight line add up to:
    A) 90° B) 180° C) 270° D) 360°

53. Two angles are supplementary. One is 75°. What is the other?
    A) 15° B) 105° C) 115° D) 285°

54. In a triangle, angles are 2x, 3x, and 4x. What is the value of x?
    A) 10° B) 20° C) 30° D) 40°

55. Vertically opposite angles are always:
    A) Supplementary B) Complementary C) Equal D) Different

56. Find angle a in this triangle with angles 40° and 60°:
    A) 60° B) 70° C) 80° D) 90°

57. Angles around a point add up to:
    A) 90° B) 180° C) 270° D) 360°

58. In a right-angled triangle, the two acute angles are:
    A) Supplementary B) Complementary C) Equal D) Both 45°

59. One angle of an isosceles triangle is 100°. What are the other two angles?
    A) 40° each B) 50° each C) 80° each D) 90° and 10°

60. Two parallel lines are crossed by a transversal. Corresponding angles are:
    A) Equal B) Supplementary C) Complementary D) None of these

61. Calculate the reflex angle if the acute angle is 35°:
    A) 35° B) 145° C) 215° D) 325°

62. In quadrilateral PQRS, angle P = 80°, Q = 100°, R = 120°. Find angle S:
    A) 40° B) 50° C) 60° D) 70°

63. Angles x and 3x are on a straight line. What is x?
    A) 30° B) 45° C) 60° D) 90°

64. True or False: An obtuse angle is between 90° and 180°.

65. One angle of a parallelogram is 70°. What are the other angles?
    A) 70°, 110°, 110° B) 70°, 70°, 110° C) 70°, 120°, 110° D) 70°, 100°, 100°

66. Find the missing angle in this triangle: 35°, 45°, ?
    A) 80° B) 90° C) 100° D) 110°

67. Two angles are complementary. Their difference is 20°. What is the larger angle?
    A) 35° B) 45° C) 55° D) 65°

68. In a regular pentagon, what is each interior angle?
    A) 72° B) 108° C) 120° D) 135°

69. Angles a, b, c are around a point. If a = 110°, b = 95°, find c:
    A) 115° B) 125° C) 135° D) 155°

70. Alternate angles formed by parallel lines are:
    A) Equal B) Supplementary C) Complementary D) Vertically opposite

71. A triangle cannot have:
    A) Two acute angles B) Two obtuse angles C) One right angle D) Three acute angles

72. Calculate the third angle in a triangle with angles 55° and 65°:
    A) 50° B) 60° C) 70° D) 80°

73. True or False: A quadrilateral can have all four angles obtuse.

74. The exterior angle of a triangle equals:
    A) Sum of two interior angles B) Sum of all interior angles C) Sum of two opposite interior angles D) 180° minus one interior angle

75. Find angle x if angles are 2x, 3x, and 5x in a triangle:
    A) 18° B) 30° C) 36° D) 45°

76. Co-interior angles between parallel lines sum to:
    A) 90° B) 180° C) 270° D) 360°

77. One angle of a rhombus is 50°. What is the adjacent angle?
    A) 40° B) 50° C) 130° D) 140°

78. How many degrees are there in a full turn?
    A) 90° B) 180° C) 270° D) 360°

79. The supplement of 45° is:
    A) 45° B) 90° C) 135° D) 180°

80. In a trapezium with one pair of parallel sides, two angles on the same side are:
    A) Equal B) Supplementary C) Complementary D) Vertically opposite

Section 4: Symmetry & Coordinates (20 Questions)

81. What is the order of rotational symmetry of a square?
    A) 1 B) 2 C) 3 D) 4

82. Point A has coordinates (3, 4). What are the coordinates of its reflection in the y-axis?
    A) (-3, 4) B) (3, -4) C) (-3, -4) D) (4, 3)

83. Which shape has infinite lines of symmetry?
    A) Square B) Circle C) Equilateral triangle D) Regular hexagon

84. The point (0, 0) is called:
    A) Origin B) Axis C) Vertex D) Midpoint

85. What is the line symmetry of the letter H?
    A) 1 B) 2 C) 3 D) 4

86. Rotate point (2, 3) 90° clockwise about the origin. What are the new coordinates?
    A) (3, -2) B) (-3, 2) C) (3, 2) D) (-2, 3)

87. Which quadrilateral has no lines of symmetry?
    A) Square B) Rectangle C) Parallelogram (general) D) Rhombus

88. Point P is (5, 2). Point Q is (9, 2). What is the length PQ?
    A) 2 B) 4 C) 6 D) 8

89. True or False: A scalene triangle has no rotational symmetry.

90. Midpoint of (2, 4) and (6, 8) is:
    A) (3, 4) B) (4, 6) C) (4, 4) D) (6, 4)

91. Which shape has rotational symmetry order 3?
    A) Square B) Equilateral triangle C) Rectangle D) Regular pentagon

92. Point in Quadrant III has coordinates:
    A) (+, +) B) (-, +) C) (-, -) D) (+, -)

93. How many lines of symmetry does a regular octagon have?
    A) 4 B) 6 C) 8 D) 10

94. Reflect point (4, -1) in the x-axis:
    A) (4, 1) B) (-4, 1) C) (-4, -1) D) (4, -1)

95. Which letter has rotational symmetry order 2?
    A) A B) H C) N D) S

96. Distance between (1, 1) and (4, 5) is:
    A) 3 B) 4 C) 5 D) 6

97. True or False: A kite always has exactly one line of symmetry.

98. What is the order of rotational symmetry of the letter Z?
    A) 0 B) 1 C) 2 D) 4

99. Point R is 3 units right and 2 units down from point (1, 5). What are its coordinates?
    A) (4, 3) B) (4, 7) C) (-2, 3) D) (-2, 7)

100. Which transformation changes (x, y) to (x, -y)?
     A) Reflection in x-axis B) Reflection in y-axis C) 90° rotation D) Translation

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Part 3: 10 Previous Year GL Assessment Questions

Question 1: The diagram shows two parallel lines crossed by a transversal. One angle is marked 65°. What is the size of angle x?
[Diagram showing parallel lines with 65° angle and angle x marked as corresponding]
A) 65° B) 115° C) 125° D) 180°

Question 2: Which 3D shape has exactly 5 faces, 8 edges, and 5 vertices?
A) Cube B) Cuboid C) Square-based pyramid D) Triangular prism

Question 3: A regular polygon has interior angles of 135°. How many sides does it have?
A) 6 B) 8 C) 10 D) 12

Question 4: *Point P has coordinates (3, -2). In which quadrant is it located?*
A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV

Question 5: The net of a 3D shape is shown. When folded, which shape does it make?
[Net showing 6 squares in a cross shape]
A) Cube B) Cuboid C) Square-based pyramid D) Tetrahedron

Question 6: In an isosceles triangle, the vertex angle is 40°. What is the size of each base angle?
A) 40° B) 60° C) 70° D) 80°

Question 7: Which quadrilateral always has diagonals that are equal in length?
A) Rhombus B) Kite C) Parallelogram D) Rectangle

Question 8: Angles around a point are 85°, 95°, 120°, and x. What is the value of x?
A) 50° B) 60° C) 70° D) 80°

Question 9: How many lines of symmetry does a regular pentagon have?
A) 3 B) 4 C) 5 D) 6

Question 10: A cube has volume 125 cm³. What is the surface area of one face?
A) 5 cm² B) 25 cm² C) 100 cm² D) 150 cm²

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Part 4: Answer Key & Detailed Solutions

Section 1 Solutions:

1. C) Scalene

2. C) 6

3. C) Trapezium

4. B) 540° ((5-2)×180 = 3×180)

5. C) 12 (Interior 150°, exterior = 30°, sides = 360÷30 = 12)

6. B) Rhombus

7. B) 40° (360÷9 = 40°)

8. True (A square has all properties of a rhombus plus right angles)

9. B) 50° ((180-80)÷2 = 50°)

10. B) 20 (n(n-3)/2 = 8×5/2 = 20)

11. B) Rectangle

12. B) Isosceles right-angled

13. D) 144° (1+2+3+4=10 parts, 360÷10=36 per part, largest=4×36=144°)

14. B) 15 (360÷24 = 15)

15. C) Opposite sides are equal

16. C) 3

17. C) 7

18. B) 70° (360-(85+95+110)=70°)

19. True

20. C) 95° and 95° (Sum of angles=360, remaining sum=190°, in kite two angles are equal)

21. C) 360°

22. C) 1440° ((10-2)×180=8×180)

23. C) Rhombus

24. D) 27.7 cm² (side=8cm, area=(√3/4)×64=16√3≈27.7)

25. True

26. Square

27. 20 (Interior=162°, exterior=18°, sides=360÷18=20)

28. D) Both B and C

29. 150° ((12-2)×180÷12=10×180÷12=150)

30. Right-angled (6²+8²=10²)

Section 2 Solutions:

31. B) 5

32. B) 6 faces, 12 edges, 8 vertices

33. B) Cylinder

34. B) 5

35. B) 4

36. [The "T" shape net cannot make a cube; cross shape can]

37. C) 60 cm³ (5×4×3)

38. C) 18

39. B) Pentagons

40. True (1 circular face, 1 curved face, 1 circular edge)

41. B) Square

42. B) 6 (Cube:12 edges, Tetrahedron:6 edges, difference=6)

43. A) 1540 cm³ (πr²h=(22/7)×49×10=1540)

44. D) 150 cm² (6×5²=6×25)

45. A) All polyhedra

46. 3

47. Pentagonal prism

48. B) 4cm (∛64=4)

49. False (Sphere has none)

50. C) Cone

Section 3 Solutions:

51. B) Obtuse

52. B) 180°

53. B) 105° (180-75)

54. B) 20° (2x+3x+4x=180, 9x=180, x=20)

55. C) Equal

56. C) 80° (180-(40+60)=80)

57. D) 360°

58. B) Complementary (sum to 90°)

59. A) 40° each (180-100=80, 80÷2=40)

60. A) Equal

61. D) 325° (360-35)

62. C) 60° (360-(80+100+120)=60)

63. B) 45° (x+3x=180, 4x=180, x=45)

64. True

65. A) 70°, 110°, 110° (Adjacent angles supplementary)

66. C) 100° (180-(35+45)=100)

67. C) 55° (x+y=90, x-y=20, solving: 2x=110, x=55)

68. B) 108° ((5-2)×180÷5=3×180÷5=108)

69. D) 155° (360-(110+95)=155)

70. A) Equal

71. B) Two obtuse angles (sum would exceed 180°)

72. B) 60° (180-(55+65)=60)

73. False (Sum would exceed 360°)

74. C) Sum of two opposite interior angles

75. A) 18° (2x+3x+5x=180, 10x=180, x=18)

76. B) 180°

77. C) 130° (Adjacent angles supplementary in rhombus)

78. D) 360°

79. C) 135° (180-45)

80. B) Supplementary

Section 4 Solutions:

81. D) 4

82. A) (-3, 4)

83. B) Circle

84. A) Origin

85. B) 2 (horizontal and vertical)

86. A) (3, -2)

87. C) Parallelogram (general)

88. B) 4 (9-5=4)

89. True

90. B) (4, 6) ((2+6)/2=4, (4+8)/2=6)

91. B) Equilateral triangle

92. C) (-, -)

93. C) 8

94. A) (4, 1)

95. C) N (also H, I, O, S, X, Z)

96. C) 5 (√[(4-1)²+(5-1)²]=√[9+16]=√25=5)

97. False (A kite can have 2 lines if it's a rhombus)

98. C) 2 (rotational symmetry of 180°)

99. A) (4, 3) (1+3=4, 5-2=3)

100. A) Reflection in x-axis

10 GL Assessment Questions Solutions:

1. A) 65° (Corresponding angles are equal with parallel lines)

2. C) Square-based pyramid (5 faces: 1 square + 4 triangles, 8 edges, 5 vertices)

3. B) 8 (Interior=135°, exterior=45°, sides=360÷45=8)

4. D) Quadrant IV (x positive, y negative)

5. A) Cube (The cross-shaped net of 6 squares folds to make a cube)

6. C) 70° ((180-40)÷2=140÷2=70)

7. D) Rectangle (Both square and rectangle have equal diagonals)

8. B) 60° (360-(85+95+120)=60)

9. C) 5 (Regular pentagon has 5 lines of symmetry)

10. B) 25 cm² (Side = ∛125=5cm, face area=5×5=25 cm²)

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Part 5: Key Revision Tips

1. Memorize these formulas:

   • Sum of interior angles = (n-2) × 180°

   • Each interior angle (regular) = (n-2) × 180° ÷ n

   • Sum of exterior angles = 360° (always!)

   • Each exterior angle (regular) = 360° ÷ n

2. Angle rules to know by heart:

   • Straight line = 180°

   • Point = 360°

   • Triangle = 180°

   • Quadrilateral = 360°

3. Symmetry facts:

   • Square: 4 lines, order 4

   • Rectangle: 2 lines, order 2

   • Rhombus: 2 lines, order 2

   • Equilateral triangle: 3 lines, order 3

   • Regular pentagon: 5 lines, order 5

4. 3D shapes vocabulary:

   • Face: Flat surface

   • Edge: Where two faces meet

   • Vertex: Corner point

   • Euler's Formula: F + V = E + 2

5. Practice with nets: Visualize how 2D nets fold into 3D shapes.

6. Coordinate rules:

   • Reflection in x-axis: (x, y) → (x, -y)

   • Reflection in y-axis: (x, y) → (-x, y)

   • Rotation 90° clockwise: (x, y) → (y, -x)

Remember: Draw diagrams whenever possible. Label angles clearly. Check your answers by making sure angle sums are correct. Practice identifying shapes from different orientations.