Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -1
Chapter: Geometry - Shapes, Angles & Polygons
Step 1: Understanding Angles
An angle is a measure of turn between two lines that meet at a point (the vertex).
Types of Angles:
Acute Angle: Less than 90°.
Right Angle: Exactly 90° (often marked with a square in a corner).
Obtuse Angle: Greater than 90° but less than 180°.
Straight Line: Exactly 180°.
Reflex Angle: Greater than 180° but less than 360°.
Full Turn: Exactly 360°.
Key Angle Facts:
Angles on a straight line add up to 180°.
e.g., If one angle is 115°, the other is 180 - 115 = 65°.
Angles around a point add up to 360°.
e.g., If three angles are 110°, 95°, and 80°, the missing angle is 360 - (110+95+80) = 75°.
Vertically opposite angles are equal. (Where two straight lines cross, the angles opposite each other are equal).
Step 2: Understanding Polygons
A polygon is a 2D shape with straight sides.
Regular Polygon: All sides are the same length and all interior angles are equal (e.g., a square).
Irregular Polygon: Sides and angles are not all equal.
Common Polygons:
Triangle: 3 sides
Quadrilateral: 4 sides
Pentagon: 5 sides
Hexagon: 6 sides
Heptagon: 7 sides
Octagon: 8 sides
Nonagon: 9 sides
Decagon: 10 sides
Key Polygon Facts:
Sum of Interior Angles:
Triangles always add up to 180°.
For any polygon, you can find the sum of interior angles by splitting it into triangles. The formula is: Sum of interior angles = (n - 2) × 180°, where
nis the number of sides.Example: A hexagon (6 sides): (6-2) × 180 = 4 × 180 = 720°.
Exterior Angles: The angles on the outside if you extend the sides. For any regular polygon, all exterior angles are equal.
Sum of exterior angles for ANY polygon is 360°.
To find one exterior angle of a regular polygon: 360° ÷ number of sides.
Example: A regular octagon: One exterior angle = 360 ÷ 8 = 45°.
Step 3: Special Triangles and Quadrilaterals
Triangles:
Equilateral: All sides equal, all angles 60°.
Isosceles: Two sides equal, two angles equal.
Scalene: All sides and angles different.
Right-Angled: Has one 90° angle.
Quadrilaterals:
Square: All sides equal, all angles 90°.
Rectangle: Opposite sides equal, all angles 90°.
Parallelogram: Opposite sides equal and parallel.
Rhombus: All sides equal, opposite angles equal (a "squashed" square).
Trapezium: One pair of parallel sides.
Kite: Two pairs of adjacent sides equal.
Step 4: Symmetry
Line Symmetry: A shape has line symmetry if you can fold it in half and both sides match exactly. The fold line is the line of symmetry.
Rotational Symmetry: A shape has rotational symmetry if it can be rotated (turned) about its centre and look the same in more than one position. The order of rotational symmetry is the number of times it fits into its own outline during a full 360° turn.
Example: A square has 4 lines of symmetry and rotational symmetry of order 4.
Practice Questions (Modelled on GL Assessment Style)
Here are 50 questions covering all the sub-topics above.
Part A: Angles (Questions 1-15)
What is the size of the angle between the hands of a clock at 3 o'clock?
An angle is 34°. What is the size of its complement? (Complementary angles add to 90°).
An angle is 112°. What is the size of its supplement? (Supplementary angles add to 180°).
Calculate the size of angle *a* in this isosceles triangle. (Base angles are 40° each).
Two angles on a straight line are 3x and 2x. What is the value of x?
Angles around a point are 95°, 80°, 70°, and *y*. Find *y*.
In a right-angled triangle, one of the other angles is 25°. What is the third angle?
In an equilateral triangle, what is the size of each interior angle?
A reflex angle is 275°. What is the corresponding acute/obtuse angle?
In a parallelogram, one angle is 65°. What are the sizes of the other three angles?
Part B: Polygons (Questions 11-30)
What is the name of a polygon with 8 sides?
What is the sum of the interior angles of a pentagon?
A regular hexagon has interior angles of 120°. What is the size of one exterior angle?
How many sides does a regular polygon have if each interior angle is 135°?
How many sides does a regular polygon have if each exterior angle is 30°?
Is a square a regular polygon? Explain why.
The interior angles of a quadrilateral are 90°, 110°, and 85°. What is the fourth angle?
A polygon has its interior angles adding up to 900°. How many sides does it have?
What is the size of an exterior angle of a regular nonagon?
True or False: A rhombus is always a regular polygon.
A triangle has angles of x, x+10, and 50°. Find the value of x.
A hexagon can be divided into how many triangles from a single vertex?
What is the order of rotational symmetry of a regular pentagon?
How many lines of symmetry does a regular hexagon have?
What is the sum of the exterior angles of a heptagon?
An irregular octagon has seven angles of 150° each. What is the size of the eighth angle?
If one exterior angle of an isosceles triangle is 110°, what are the two possible sizes of the interior angles at the base?
A polygon has 15 sides. What is the sum of its interior angles?
The interior angle of a regular polygon is twice its exterior angle. How many sides does it have?
Three of the angles in a pentagon are 100°. The other two angles are equal. What is the size of one of these equal angles?
Part C: 2D Shapes & Properties (Questions 31-50)
How many pairs of parallel sides does a trapezium have?
What is the specific name for a quadrilateral with all sides equal and all angles 90°?
What type of triangle has no lines of symmetry?
A kite has one line of symmetry. If one of its angles is 90°, what could the other angles be? (Give one example).
How many right angles does a parallelogram have?
What is the difference between a rhombus and a square?
A shape has rotational symmetry of order 2 and 2 lines of symmetry. What could it be?
Draw a scalene triangle with one obtuse angle.
True or False: Every rectangle is a parallelogram.
What is the order of rotational symmetry of an isosceles triangle?
A quadrilateral has exactly two lines of symmetry and rotational symmetry of order 2. What is its name?
How many sides does a decagon have?
All rectangles are quadrilaterals. Are all quadrilaterals rectangles?
What is the size of one interior angle of a regular octagon?
A heptagon has how many diagonals? (A diagonal is a line connecting two non-adjacent vertices).
A shape is made by putting two equilateral triangles together. What is the name of the new quadrilateral formed?
What is the size of angle *b* in a right-angled isosceles triangle?
A polygon has an interior angle sum of 1800°. How many sides does it have?
True or False: A circle has infinite lines of symmetry.
A regular polygon has an exterior angle of 20°. What is the sum of its interior angles?
10 Questions from Previous Year GL Assessment Style (with Solutions)
The diagram shows an isosceles triangle. The base angles are both 55°. What is the size of the third angle?
A) 55°
B) 60°
C) 70°
D) 80°
What is the name of a polygon in which the interior angles add up to 720°?
A) Pentagon
B) Hexagon
C) Heptagon
D) Octagon
A regular polygon has an exterior angle of 40°. How many sides does it have?
A) 7
B) 8
C) 9
D) 10
The sizes of three of the angles in a quadrilateral are 100°, 110°, and 85°. What is the size of the fourth angle?
A) 55°
B) 65°
C) 75°
D) 85°
What is the order of rotational symmetry of a rectangle?
A) 1
B) 2
C) 3
D) 4
The interior angle of a regular polygon is 150°. How many sides does it have?
A) 10
B) 12
C) 15
D) 18
The diagram shows a kite. One angle is 120° and another is 50°. What is the size of the smallest angle in the kite?
A) 50°
B) 60°
C) 70°
D) 80°
How many lines of symmetry does a regular pentagon have?
A) 3
B) 4
C) 5
D) 6
Two angles are supplementary. One angle is five times the size of the other. What is the size of the larger angle?
A) 30°
B) 120°
C) 150°
D) 160°
The exterior angle of an equilateral triangle is 120°. What is the sum of the exterior angles of the triangle?
A) 120°
B) 240°
C) 360°
D) 720°
Answer Key & Solutions
Part A & B & C (Questions 1-50) -
Part A: Angles (Questions 1–10)
1. Angle between clock hands at 3 o’clock
At 3:00, hour hand at 3, minute hand at 12.
Each hour mark = 30° (360°/12).
From 12 to 3 → .
Answer: 90°
2. Complement of 34°
Complementary sum = 90°.
.
Answer: 56°
3. Supplement of 112°
Supplementary sum = 180°.
.
Answer: 68°
4. Isosceles triangle, base angles each 40°
Angles sum to 180°, so → → .
Answer: 100°
5. Two angles on a straight line: 3x and 2x
→ → .
Answer: 36
6. Angles around a point: 95°, 80°, 70°, y
Sum = 360°.
→ → .
Answer: 115°
7. Right-angled triangle, one other angle = 25°
→ → third = 65°.
Answer: 65°
8. Equilateral triangle interior angle
Each angle = 60°.
Answer: 60°
9. Reflex angle 275°, corresponding acute/obtuse angle
Reflex + other angle = 360°.
Other angle = (acute).
Answer: 85°
10. Parallelogram with one angle 65°
Opposite angles equal, adjacent supplementary.
So angles: .
Answer: 65°, 115°, 65°, 115°
Part B: Polygons (Questions 11–30)
11. Polygon with 8 sides
Octagon.
Answer: Octagon
12. Sum interior angles of pentagon
Pentagon has 5 sides. Sum = .
Answer: 540°
13. Regular hexagon interior = 120°, exterior angle
Exterior = 180 - interior = .
Answer: 60°
14. Regular polygon, interior 135°, how many sides?
Exterior = .
Number of sides .
Answer: 8
15. Regular polygon exterior = 30°, sides?
.
Answer: 12
16. Is a square a regular polygon?
Yes: all sides equal, all angles equal.
Answer: Yes — all sides and angles equal
17. Quadrilateral angles 90°, 110°, 85°, fourth angle
Sum = 360°.
→ → .
Answer: 75°
18. Interior sum = 900°, number of sides
→ → .
Answer: 7
19. Exterior angle of regular nonagon (9 sides)
Exterior = .
Answer: 40°
20. Rhombus always a regular polygon?
No — a rhombus has equal sides but not necessarily equal angles unless it’s a square.
Answer: False
21. Triangle angles x, x+10, 50°, find x
→ → → .
Answer: 60
22. Hexagon divided into triangles from one vertex
From one vertex: diagonals → triangles for interior sum. For hexagon (n=6), triangles = (not from one vertex — wait, actually they ask: "A hexagon can be divided into how many triangles from a single vertex?" From single vertex, you can draw diagonals to other non-adjacent vertices, giving triangles that include that vertex: number of triangles = triangles for interior sum, but in drawing from one vertex? Actually: A single vertex connects to n-2 others to form n-2 triangles? Misleading wording. Possibly they mean “dividing polygon into triangles by drawing non-intersecting diagonals from one vertex” — yes, that yields n-2 triangles.
For hexagon, . But that’s from one vertex for all non-intersecting diagonals from it.
Answer: 4
23. Rotational symmetry order of regular pentagon
Rotates into itself 5 times in 360°. Order = 5.
Answer: 5
24. Lines of symmetry of regular hexagon
6 lines (through opposite vertices and through midpoints of opposite sides).
Answer: 6
25. Sum exterior angles of a heptagon
Sum exterior angles of any polygon = 360°.
Answer: 360°
26. Irregular octagon: seven angles 150° each, eighth angle
Sum interior = .
Seven angles sum = .
Eighth = .
Answer: 30°
27. Isosceles triangle, one exterior angle 110°, possible base interior angles
Exterior 110° → adjacent interior = 70°.
Case 1: 70° is vertex angle → base angles = each.
Case 2: 70° is a base angle → vertex = 40°, other base = 70°.
So base angles possible: 55°, 55° or 70°, 70°. Wait, but the question asks for “two possible sizes of the interior angles at the base” — meaning in the two cases, the base angles are either (55°,55°) or (70°,70°)? But 70°,70° means vertex=40°, works fine. So possible base angle size = 55° or 70°.
Answer: 55° and 70° (two possible base angles depending on case)
28. 15 sides, sum interior angles
Sum = .
Answer: 2340°
29. Interior angle = 2 × exterior angle
Let exterior = e, interior = 2e, so → → .
Number of sides .
Answer: 6
30. Pentagon: three angles 100°, other two equal
Sum interior = 540°.
Three angles sum = 300°. Remainder = 240° for two equal angles → each = 120°.
Answer: 120°
Part C: 2D Shapes & Properties (Questions 31–50)
31. Trapezium parallel sides
A trapezium (UK) has exactly 1 pair of parallel sides.
Answer: 1 pair
32. Quadrilateral, all sides equal, all angles 90°
Square.
Answer: Square
33. Triangle with no lines of symmetry
Scalene triangle (all sides different, no symmetry).
Answer: Scalene triangle
34. Kite, one line symmetry, one angle 90°, example others
In kite, symmetry line through unequal angles; if 90° is at one of equal-angle pair?
Possible: 90°, 90°, x, y with x=y? No, kite has two equal angles. Let’s say 90° and 90° are the unequal ones? Not possible — unequal angles are not necessarily 90°. Better: 90°, 100°, 90°, 80° (90°,90° are adjacent around line of symmetry? Not both equal? A kite has one pair equal angles.) But with 90° as one angle, others could be e.g. 90°, 110°, 70°, 90° — but that’s two 90°. Acceptable. One example: 90°, 90°, 120°, 60° (not possible sum 360). Let’s compute:
Example: 90°, 90°, 100°, 80° sum=360. Equal angles could be 90° each (the pair of equal angles are opposite? no, adjacent). So: 90°, 90°, then the other pair equal 100°, 80°? That’s not equal pair — so must be 90° and 90° are the equal ones → other two unequal sum 180: e.g. 100°, 80°. Works.
Answer: e.g. 90°, 90°, 100°, 80°
35. Right angles in a parallelogram
A general parallelogram has 0 right angles unless it’s a rectangle.
Answer: 0 (unless rectangle)
36. Difference rhombus and square
Both have all sides equal, but square has all angles 90°, rhombus does not necessarily.
Answer: A square has all angles 90°, rhombus doesn’t
37. Rotational symmetry order 2, 2 lines of symmetry
Rectangle.
Answer: Rectangle
38. Draw scalene triangle with one obtuse angle
Cannot draw here, but description: all sides different, one angle > 90°.
39. Every rectangle is a parallelogram
True — opposite sides parallel.
Answer: True
40. Rotational symmetry order of isosceles triangle
Order 1 (no rotation except 360°), unless equilateral.
Answer: 1
41. Quadrilateral, 2 lines symmetry, order 2 rotational
Rhombus (rectangle has order 2 but 2 lines symmetry for non-square? Actually square has 4 lines. Rectangle has 2 lines if not square. Rhombus if not square has 2 lines symmetry? Yes, diagonals are symmetry lines, order 2 rotation). Possible also oblong rectangle? But oblong rectangle fits: 2 lines symmetry through midpoints, rotational order 2. They might be thinking of rhombus, but rectangle also fits. But rhombus’s lines of symmetry are diagonals (if square) only if angles 90°? Wait, in a rhombus (not square), lines of symmetry are diagonals? No, a rhombus that’s not square has no lines of symmetry? Actually a rhombus has 2 lines of symmetry only if it’s a square? Correction: kite has one line. I think they intend rectangle (non-square).
Let’s check:
Rectangle: 2 lines (midpoints), order 2 rotation.
Rhombus (non-square): 2 lines of symmetry through opposite vertices, order 2 rotation.
Both fit, but a rhombus (non-square) has axes along diagonals, yes, and order 2 rotation.
Common exam answer: Rhombus.
Answer: Rhombus
42. Decagon sides
10 sides.
Answer: 10
43. All rectangles are quadrilaterals, are all quadrilaterals rectangles?
No — quadrilaterals include trapeziums, kites, etc.
Answer: No
44. Interior angle of regular octagon
Each interior = .
Answer: 135°
45. Heptagon diagonals
Number of diagonals = .
Answer: 14
46. Two equilateral triangles together (edge sharing) → quadrilateral
Putting base-to-base → rhombus (parallelogram with 60° and 120° angles).
Answer: Rhombus
47. Right-angled isosceles triangle angles
90°, 45°, 45°. b likely refers to one base angle = 45°.
Answer: 45°
48. Interior sum 1800°, sides
→ → .
Answer: 12
49. Circle lines of symmetry
Infinite lines through center.
Answer: True
50. Regular polygon exterior = 20°, sum interior angles
sides.
Sum interior = .
Answer: 2880°
10 GL Assessment Style Questions:
C) 70° (180 - 55 - 55 = 70)
B) Hexagon ((n-2)×180=720 → n-2=4 → n=6)
C) 9 (Number of sides = 360 ÷ 40 = 9)
B) 65° (Sum of quadrilateral angles=360°. 360 - (100+110+85)=65)
B) 2 (It looks the same in 2 positions: upright and at 180°)
B) 12 (Exterior angle = 180-150=30°. Sides=360/30=12)
A) 50° (In a kite, two angles are equal and two are different. The 50° angle will have a matching 50° angle. Total = 120+50+50 + x = 360 → x=140. The smallest angles are the two 50° ones).
C) 5
C) 150° (Let smaller angle = x. Larger = 5x. x + 5x = 180 → 6x=180 → x=30. Larger angle=5×30=150)
C) 360° (The sum of exterior angles for ANY polygon is always 360°).
