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

Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -1

 

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 n is 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.

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Practice Questions (Modelled on GL Assessment Style)

Here are 50 questions covering all the sub-topics above.

Part A: Angles (Questions 1-15)

1. What is the size of the angle between the hands of a clock at 3 o'clock?

2. An angle is 34°. What is the size of its complement? (Complementary angles add to 90°).

3. An angle is 112°. What is the size of its supplement? (Supplementary angles add to 180°).

4. Calculate the size of angle *a* in this isosceles triangle. (Base angles are 40° each).

5. Two angles on a straight line are 3x and 2x. What is the value of x?

6. Angles around a point are 95°, 80°, 70°, and *y*. Find *y*.

7. In a right-angled triangle, one of the other angles is 25°. What is the third angle?

8. In an equilateral triangle, what is the size of each interior angle?

9. A reflex angle is 275°. What is the corresponding acute/obtuse angle?

10. In a parallelogram, one angle is 65°. What are the sizes of the other three angles?

Part B: Polygons (Questions 11-30)

11. What is the name of a polygon with 8 sides?

12. What is the sum of the interior angles of a pentagon?

13. A regular hexagon has interior angles of 120°. What is the size of one exterior angle?

14. How many sides does a regular polygon have if each interior angle is 135°?

15. How many sides does a regular polygon have if each exterior angle is 30°?

16. Is a square a regular polygon? Explain why.

17. The interior angles of a quadrilateral are 90°, 110°, and 85°. What is the fourth angle?

18. A polygon has its interior angles adding up to 900°. How many sides does it have?

19. What is the size of an exterior angle of a regular nonagon?

20. True or False: A rhombus is always a regular polygon.

21. A triangle has angles of x, x+10, and 50°. Find the value of x.

22. A hexagon can be divided into how many triangles from a single vertex?

23. What is the order of rotational symmetry of a regular pentagon?

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

25. What is the sum of the exterior angles of a heptagon?

26. An irregular octagon has seven angles of 150° each. What is the size of the eighth angle?

27. If one exterior angle of an isosceles triangle is 110°, what are the two possible sizes of the interior angles at the base?

28. A polygon has 15 sides. What is the sum of its interior angles?

29. The interior angle of a regular polygon is twice its exterior angle. How many sides does it have?

30. 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)

31. How many pairs of parallel sides does a trapezium have?

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

33. What type of triangle has no lines of symmetry?

34. A kite has one line of symmetry. If one of its angles is 90°, what could the other angles be? (Give one example).

35. How many right angles does a parallelogram have?

36. What is the difference between a rhombus and a square?

37. A shape has rotational symmetry of order 2 and 2 lines of symmetry. What could it be?

38. Draw a scalene triangle with one obtuse angle.

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

40. What is the order of rotational symmetry of an isosceles triangle?

41. A quadrilateral has exactly two lines of symmetry and rotational symmetry of order 2. What is its name?

42. How many sides does a decagon have?

43. All rectangles are quadrilaterals. Are all quadrilaterals rectangles?

44. What is the size of one interior angle of a regular octagon?

45. A heptagon has how many diagonals? (A diagonal is a line connecting two non-adjacent vertices).

46. A shape is made by putting two equilateral triangles together. What is the name of the new quadrilateral formed?

47. What is the size of angle *b* in a right-angled isosceles triangle?

48. A polygon has an interior angle sum of 1800°. How many sides does it have?

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

50. A regular polygon has an exterior angle of 20°. What is the sum of its interior angles?

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10 Questions from Previous Year GL Assessment Style (with Solutions)

1. 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°

2. What is the name of a polygon in which the interior angles add up to 720°?

   • A) Pentagon

   • B) Hexagon

   • C) Heptagon

   • D) Octagon

3. A regular polygon has an exterior angle of 40°. How many sides does it have?

   • A) 7

   • B) 8

   • C) 9

   • D) 10

4. 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°

5. What is the order of rotational symmetry of a rectangle?

   • A) 1

   • B) 2

   • C) 3

   • D) 4

6. The interior angle of a regular polygon is 150°. How many sides does it have?

   • A) 10

   • B) 12

   • C) 15

   • D) 18

7. 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°

8. How many lines of symmetry does a regular pentagon have?

   • A) 3

   • B) 4

   • C) 5

   • D) 6

9. 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°

10. 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°

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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 → $3\times 30\mathrm{°}=90\mathrm{°}$.
Answer: 90°

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2. Complement of 34°
Complementary sum = 90°.
$90-34=56\mathrm{°}$.
Answer: 56°

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3. Supplement of 112°
Supplementary sum = 180°.
$180-112=68\mathrm{°}$.
Answer: 68°

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4. Isosceles triangle, base angles each 40°
Angles sum to 180°, so $a+40+40=180$ → $a+80=180$ → $a=100\mathrm{°}$.
Answer: 100°

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5. Two angles on a straight line: 3x and 2x
$3x+2x=180\mathrm{°}$ → $5x=180$ → $x=36$.
Answer: 36

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6. Angles around a point: 95°, 80°, 70°, y
Sum = 360°.
$95+80+70+y=360$ → $245+y=360$ → $y=115\mathrm{°}$.
Answer: 115°

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7. Right-angled triangle, one other angle = 25°
$90+25+\text{third}=180$ → $115+\text{third}=180$ → third = 65°.
Answer: 65°

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8. Equilateral triangle interior angle
Each angle = 60°.
Answer: 60°

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9. Reflex angle 275°, corresponding acute/obtuse angle
Reflex + other angle = 360°.
Other angle = $360-275=85\mathrm{°}$ (acute).
Answer: 85°

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10. Parallelogram with one angle 65°
Opposite angles equal, adjacent supplementary.
So angles: $65\mathrm{°},115\mathrm{°},65\mathrm{°},115\mathrm{°}$.
Answer: 65°, 115°, 65°, 115°

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Part B: Polygons (Questions 11–30)

11. Polygon with 8 sides
Octagon.
Answer: Octagon

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12. Sum interior angles of pentagon
Pentagon has 5 sides. Sum = $(5-2)\times 180=3\times 180=540\mathrm{°}$.
Answer: 540°

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13. Regular hexagon interior = 120°, exterior angle
Exterior = 180 - interior = $180-120=60\mathrm{°}$.
Answer: 60°

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14. Regular polygon, interior 135°, how many sides?
Exterior = $180-135=45\mathrm{°}$.
Number of sides $n=360\mathrm{/}45=8$.
Answer: 8

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15. Regular polygon exterior = 30°, sides?
$n=360\mathrm{/}30=12$.
Answer: 12

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16. Is a square a regular polygon?
Yes: all sides equal, all angles equal.
Answer: Yes — all sides and angles equal

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17. Quadrilateral angles 90°, 110°, 85°, fourth angle
Sum = 360°.
$90+110+85+x=360$ → $285+x=360$ → $x=75\mathrm{°}$.
Answer: 75°

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18. Interior sum = 900°, number of sides
$(n-2)\times 180=900$ → $n-2=5$ → $n=7$.
Answer: 7

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19. Exterior angle of regular nonagon (9 sides)
Exterior = $360\mathrm{/}9=40\mathrm{°}$.
Answer: 40°

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20. Rhombus always a regular polygon?
No — a rhombus has equal sides but not necessarily equal angles unless it’s a square.
Answer: False

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21. Triangle angles x, x+10, 50°, find x
$x+(x+10)+50=180$ → $2x+60=180$ → $2x=120$ → $x=60$.
Answer: 60

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22. Hexagon divided into triangles from one vertex
From one vertex: $n-3$ diagonals → $n-2$ triangles for interior sum. For hexagon (n=6), triangles = $4$ (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 = $n-2=4$ 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, $n-2=4$. But that’s from one vertex for all non-intersecting diagonals from it.
Answer: 4

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23. Rotational symmetry order of regular pentagon
Rotates into itself 5 times in 360°. Order = 5.
Answer: 5

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24. Lines of symmetry of regular hexagon
6 lines (through opposite vertices and through midpoints of opposite sides).
Answer: 6

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25. Sum exterior angles of a heptagon
Sum exterior angles of any polygon = 360°.
Answer: 360°

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26. Irregular octagon: seven angles 150° each, eighth angle
Sum interior = $(8-2)\times 180=1080\mathrm{°}$.
Seven angles sum = $7\times 150=1050$.
Eighth = $1080-1050=30\mathrm{°}$.
Answer: 30°

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27. Isosceles triangle, one exterior angle 110°, possible base interior angles
Exterior 110° → adjacent interior = 70°.
Case 1: 70° is vertex angle → base angles = $(180-70)\mathrm{/}2=55\mathrm{°}$ 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)

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28. 15 sides, sum interior angles
Sum = $(15-2)\times 180=13\times 180=2340\mathrm{°}$.
Answer: 2340°

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29. Interior angle = 2 × exterior angle
Let exterior = e, interior = 2e, so $2e+e=180\mathrm{°}$ → $3e=180$ → $e=60\mathrm{°}$.
Number of sides $n=360\mathrm{/}60=6$.
Answer: 6

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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°

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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

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32. Quadrilateral, all sides equal, all angles 90°
Square.
Answer: Square

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33. Triangle with no lines of symmetry
Scalene triangle (all sides different, no symmetry).
Answer: Scalene triangle

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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°

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35. Right angles in a parallelogram
A general parallelogram has 0 right angles unless it’s a rectangle.
Answer: 0 (unless rectangle)

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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

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37. Rotational symmetry order 2, 2 lines of symmetry
Rectangle.
Answer: Rectangle

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38. Draw scalene triangle with one obtuse angle
Cannot draw here, but description: all sides different, one angle > 90°.

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39. Every rectangle is a parallelogram
True — opposite sides parallel.
Answer: True

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40. Rotational symmetry order of isosceles triangle
Order 1 (no rotation except 360°), unless equilateral.
Answer: 1

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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

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42. Decagon sides
10 sides.
Answer: 10

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43. All rectangles are quadrilaterals, are all quadrilaterals rectangles?
No — quadrilaterals include trapeziums, kites, etc.
Answer: No

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44. Interior angle of regular octagon
Each interior = $180-(360\mathrm{/}8)=180-45=135\mathrm{°}$.
Answer: 135°

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45. Heptagon diagonals
Number of diagonals = $n(n-3)\mathrm{/}2=7\times 4\mathrm{/}2=14$.
Answer: 14

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46. Two equilateral triangles together (edge sharing) → quadrilateral
Putting base-to-base → rhombus (parallelogram with 60° and 120° angles).
Answer: Rhombus

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47. Right-angled isosceles triangle angles
90°, 45°, 45°. b likely refers to one base angle = 45°.
Answer: 45°

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48. Interior sum 1800°, sides
$(n-2)\times 180=1800$ → $n-2=10$ → $n=12$.
Answer: 12

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49. Circle lines of symmetry
Infinite lines through center.
Answer: True

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50. Regular polygon exterior = 20°, sum interior angles
$n=360\mathrm{/}20=18$ sides.
Sum interior = $(18-2)\times 180=16\times 180=2880\mathrm{°}$.
Answer: 2880°

10 GL Assessment Style Questions:

1. C) 70° (180 - 55 - 55 = 70)

2. B) Hexagon ((n-2)×180=720 → n-2=4 → n=6)

3. C) 9 (Number of sides = 360 ÷ 40 = 9)

4. B) 65° (Sum of quadrilateral angles=360°. 360 - (100+110+85)=65)

5. B) 2 (It looks the same in 2 positions: upright and at 180°)

6. B) 12 (Exterior angle = 180-150=30°. Sides=360/30=12)

7. 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).

8. C) 5

9. C) 150° (Let smaller angle = x. Larger = 5x. x + 5x = 180 → 6x=180 → x=30. Larger angle=5×30=150)

10. C) 360° (The sum of exterior angles for ANY polygon is always 360°).