Comprehensive assessment covering all 20 lessons. Mixed practice across angles and lines, triangles, quadrilaterals, polygons, congruence, similarity and constructions.
Question 16 3 marks
(a) Two angles lie on a straight line. One is 113°. Find the other. 1 mark
(b) Three angles meet at a point: 150°, 90° and z. Find z. 1 mark
(c) Two angles in a triangle are 35° and 95°. Find the third angle. 1 mark
(a) Angles on a straight line add to 180°: 180 − 113 = 67° [1]
(b) Angles at a point add to 360°: 360 − 150 − 90 = 120° [1]
(c) Angle sum of a triangle is 180°: 180 − 35 − 95 = 50° [1]
Question 17 4 marks
(a) An exterior angle of a triangle equals the sum of the two opposite interior angles 70° and 55°. Find the exterior angle. 2 marks
(b) An isosceles triangle has an apex angle of 50°. Find the size of each equal base angle. 2 marks
(a) Exterior angle = 70 + 55 = 125° [2]
(b) Base angles are equal and the three angles add to 180°: (180 − 50) ÷ 2 = 65° each [2]
Question 18 4 marks
(a) Name a quadrilateral with exactly one pair of parallel sides. 1 mark
(b) A transversal crosses two parallel lines. The co-interior angle of a 105° angle is x. Find x. 1 mark
(c) Three angles of a quadrilateral are 90°, 110° and 85°. Find the fourth angle. 1 mark
(d) A transversal crosses two parallel lines. The corresponding angle of a 62° angle is y. Find y. 1 mark
(a) Trapezium [1]
(b) Co-interior angles are supplementary: x = 180 − 105 = 75° [1]
(c) Angle sum of a quadrilateral is 360°: 360 − 90 − 110 − 85 = 75° [1]
(d) Corresponding angles are equal: y = 62° [1]
Question 19 4 marks
(a) Find the sum of the interior angles of a heptagon (7 sides). 1 mark
(b) A regular polygon has an exterior angle of 45°. How many sides does it have? 1 mark
(c) Two triangles are similar with scale factor 2. A side on the smaller triangle is 9 cm. Find the matching side on the larger triangle. 2 marks
(a) (n − 2) × 180° = (7 − 2) × 180 = 900° [1]
(b) Exterior angles sum to 360°: 360 ÷ 45 = 8 sides [1]
(c) Matching side = 9 × 2 = 18 cm [2]
Question 20 5 marks
(a) A triangle has sides 8 cm, 8 cm and 8 cm. Classify it by its sides and by its angles. 2 marks
(b) Find the size of each interior angle of a regular pentagon. 1 mark
(c) A 1.5 m fence post casts a 2 m shadow. At the same time a flagpole casts an 8 m shadow. Use similar triangles to find the height of the flagpole. 1 mark
(d) Explain the difference between two figures being congruent and being similar. 1 mark
(a) All three sides equal, so it is equilateral by sides; each angle is 180 ÷ 3 = 60°, so it is acute by angles [2]
(b) Interior angle sum = (5 − 2) × 180 = 540°; each angle = 540 ÷ 5 = 108° [1]
(c) height ÷ shadow is constant: 1.5 ÷ 2 = 0.75; flagpole height = 0.75 × 8 = 6 m [1]
(d) Congruent figures have the same shape AND the same size; similar figures have the same shape but can be different sizes (sides in a constant ratio) [1]