Angles in Triangles and Quadrilaterals: Full Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8–9 · Geometry

Angles in Triangles and Quadrilaterals: Full Guide

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

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.

1
A triangle has angles 55°, 65° and x. Find x. (basic)
(2)
180° − 55° − 65° = 60°✓✓ (2)
2
A right-angled triangle has one other angle of 35°. Find the third. (right-angled)
(2)
180° − 90° − 35° = 55°✓✓ (2)
3
Isosceles triangle, apex 80°. Find each base angle. (isosceles)
(2)
(180° − 80°) ÷ 2 = 50°✓✓ (2)
4
Isosceles triangle, base angles 65° each. Find the apex. (isosceles)
(2)
180° − 65° − 65° = 50°✓✓ (2)
5
Interior angles 70° and 50°; find the exterior angle at the third vertex. (exterior)
(2)
70° + 50° = 120°✓✓ (2)
6
Triangle angles are x, x and 4x. Find x. (solve)
(2)
6x = 180 → x = 30°✓✓ (2)
7
Triangle angles are 2x, 3x and 4x. Find the largest angle. (solve)
(2)
9x = 180 → x = 20; largest 4x = 80°✓✓ (2)
8
Quadrilateral angles 120°, 80°, 70° and x. Find x. (quad)
(2)
360° − 270° = 90°✓✓ (2)
9
In parallelogram ABCD below, Â = 110°. Determine the size of x, giving a reason.
(2)
180° − 110° = 70°✓✓ (2)
10
Two angles of a triangle are equal; the third is 80°. Find each equal angle. (isosceles)
(2)
(180° − 80°) ÷ 2 = 50°✓✓ (2)

TOTAL: 20 marks