∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 8–9 · Geometry of 2D Shapes
Angles in Triangles and Quadrilaterals: Full Guide
MEMORANDUM
Name:
Class:
Date:
Mark
/ 26
Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.
- 1Two angles of a triangle (the third is 30°) are (2x + 10)° and (4x + 20)°. Determine the value of x, and hence the size of each angle.(4)The angles of a triangle add up to 180°, so these two add to 150° (1)
6x + 30 = 150 (1)
x = 20 (1)
The angles are 50° and 100° (1)✓✓✓✓ (4) - 2A triangle has angles 55°, 65° and x. Find x. (basic)(1)180° − 55° − 65° = 60°✓ (1)
- 3A right-angled triangle has one other angle of 35°. Find the third. (right-angled)(2)180° − 90° − 35° = 55°✓✓ (2)
- 4Isosceles triangle, apex 80°. Find each base angle. (isosceles)(2)(180° − 80°) ÷ 2 = 50°✓✓ (2)
- 5Isosceles triangle, base angles 65° each. Find the apex. (isosceles)(2)180° − 65° − 65° = 50°✓✓ (2)
- 6Interior angles 70° and 50°; find the exterior angle at the third vertex. (exterior)(2)70° + 50° = 120°✓✓ (2)
- 7Triangle angles are x, x and 4x. Find x. (solve)(3)6x = 180 → x = 30°✓✓✓ (3)
- 8Triangle angles are 2x, 3x and 4x. Find the largest angle. (solve)(3)9x = 180 → x = 20; largest 4x = 80°✓✓✓ (3)
- 9Quadrilateral angles 120°, 80°, 70° and x. Find x. (quad)(2)360° − 270° = 90°✓✓ (2)
- 10In parallelogram ABCD below, Â = 110°. Determine the size of x, giving a reason.(3)180° − 110° = 70°✓✓✓ (3)
- 11Two angles of a triangle are equal; the third is 80°. Find each equal angle. (isosceles)(2)(180° − 80°) ÷ 2 = 50°✓✓ (2)
TOTAL: 26 marks