"Geometry: Shapes & Angles, Polygons"
GL Assessment 11+ exam for schools
### **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**.
---
### **Practice Questions (Modelled on GL Assessment Style)**
#### **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?
---
### **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°
---
### **Answer Key & Solutions**
**Part A & B & C (Questions 1-50) - Selected Solutions:**
* **2.** Complement = 90° - 34° = **56°**
* **4.** Sum of angles in triangle = 180°. 180 - (40+40) = **100°**
* **5.** 3x + 2x = 180 → 5x=180 → x=**36**
* **13.** Exterior angle = 180 - 120 = **60°** (Or 360/6=**60°**)
* **14.** If interior is 135°, exterior is 45°. Sides = 360/45 = **8 sides**
* **18.** (n-2)×180=900 → n-2=5 → n=**7 sides**
* **29.** Let exterior = x. Interior = 2x. So x + 2x = 180 → 3x=180 → x=60. Sides=360/60=**6 sides**.
* **30.** Sum of pentagon angles=540°. Three angles=300°. Remaining=240°. Two equal angles=240/2=**120°**.
* **45.** Diagonals = n(n-3)/2. For heptagon (7 sides): 7×4/2=**14**.
* **48.** (n-2)×180=1800 → n-2=10 → n=**12 sides**.
**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°).
### **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?
### **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 Ο=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
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### **Answer Key & Solutions**
**Section A:**
1. Reflex
2. Acute
3. Obtuse
4. 4
5. 53°
6. 60° (x + 2x = 180, 3x=180, x=60)
7. 60°
8. 115° (360 - 245 = 115)
9. D (30+70+100=200, not 180)
10. 72° (360 ÷ 5)
**Section B:**
11. 900° ((7-2)x180=5x180)
12. 15 (360 ÷ 24)
13. 110° (Pentagon sum=540, 540-(100+110+115+105)=110)
14. Nonagon
15. Yes. (Ext=10°, sides=360/10=36 sides. A triacontakaihexagon.)
16. 3
17. 9 ((n-2)x180=1260, n-2=7, n=9)
18. 8
19. Decagon (Int=144, Ext=36, sides=360/36=10)
20. False
**Section C:**
21. Scalene
22. 40°, Isosceles
23. 3
24. 4
25. Trapezium
26. No
27. No
28. Parallelogram
29. 75°, 105°, 105° (Adjacent angles supplementary)
30. It can have 0, 1, or 2 (but not 3 or 4).
31. Scalene has no equal sides/angles; Isosceles has 2 equal sides/angles.
32. (A quadrilateral with one pair of parallel sides)
33. Isosceles
34. False (angles not necessarily 90°)
35. 60°
36. Square
37. 2
38. 360°
39. Square
40. True
41. 70° ((180-40)/2)
42. 26cm (2*(8+5))
43. 81cm² (side=9cm, area=9x9)
44. 4cm (Area = base x height, 20=5xh, h=4)
45. 8 cm² (Base=3, Height=4, Area=0.5x3x4=6? Wait, vertices (1,1), (1,5), (4,1). Base from (1,1) to (4,1) is 3. Height from (1,5) to y=1 is 4. Area=0.5*3*4=6. My question is wrong, answer should be 6cm². Let's correct it to 6cm²).
46. Hypotenuse
47. 80°, Scalene
48. Rhombus
49. 7
50. True
51. 8 (Int=135, Ext=45, sides=360/45)
52. 40° (360/9)
53. Isosceles
54. Right-angled (3²+4²=5²)
55. Square
56. Rhombus
57. 6
58. 3
59. True
60. Parallelogram (if not a rectangle/rhombus)
61. 5cm (Area=0.5xbxh, 15=0.5x6xh, 15=3h, h=5)
62. 28cm (side=7cm, perimeter=4x7)
63. 4cm (P=2(l+w), 24=2(8+w), 12=8+w, w=4)
64. 30cm² (10x3)
65. 32cm² (0.5*(6+10)*4)
66. Acute-angled
67. Obtuse-angled
68. True
69. 5
70. Square
**Section D (Sample):**
71. 55° (180-125)
72. 110° (360-(100+150))
73. 40°, 140°, 140° (Vertically opposite, then supplementary)
98. 120° (Let base=x. Vertex=4x. x+x+4x=180, 6x=180, x=30. Vertex=4*30=120)
100. 45° each ((180-90)/2)
**Section E:**
101. 6
102. 12
103. 5
104. Cone
105. 9
106. Equilateral Triangles
107. 2
108. Cuboid
109. 1
110. 8
127. 282.6 cm³ (V=Οr²h=3.14*9*10)
**Sections F & G:**
181. C
182. B
183. C
184. D
185. B
186. A
187. C
188. C
189. C
190. C
229. C (8-2=6)
230. D ((1/6)*(1/6)=1/36)
