Covers Lessons 1–7: angles and lines, classifying triangles by their sides and angles, the angle sum of a triangle, exterior angles, triangle problem solving and an introduction to quadrilaterals.
Question 9 3 marks
(a) Two angles sit on a straight line. One is 118°. Find the other angle. 1 mark
(b) Two angles in a triangle are 50° and 60°. Find the third angle. 1 mark
(c) An exterior angle of a triangle equals the sum of the two opposite interior angles 64° and 58°. Find the exterior angle. 1 mark
(a) Angles on a straight line add to 180°: 180 − 118 = 62° [1]
(b) Angle sum of a triangle is 180°: 180 − 50 − 60 = 70° [1]
(c) Exterior angle = 64 + 58 = 122° [1]
Question 10 3 marks
A triangle has sides of length 7 cm, 7 cm and 4 cm. Its apex angle (between the two equal sides) is 40°.
(a) Classify this triangle by its sides. 1 mark
(b) Find the size of each equal base angle. 2 marks
(a) Two sides are equal (7 cm and 7 cm), so it is isosceles [1]
(b) The base angles are equal and the three angles add to 180°: (180 − 40) ÷ 2 = 140 ÷ 2 = 70° each [2]
Question 11 4 marks
The three angles of a triangle are x, x + 20° and x + 40°.
(a) Write an equation and solve it to find x. 2 marks
(b) State the size of all three angles. 2 marks
(a) x + (x + 20) + (x + 40) = 180, so 3x + 60 = 180, 3x = 120, x = 40° [2]
(b) The angles are 40°, 60° and 80° (check: 40 + 60 + 80 = 180°) [2]