Angles on Parallel Lines: The Complete Exam Guide — Worksheet & Memo

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Grade 8–9 · Geometry

Angles on Parallel Lines: The Complete Exam 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
In the diagram below, AB ∥ CD. Determine the size of x, giving a reason.
(2)
x = 65° (alt ∠s; AB ∥ CD)✓✓ (2)
2
In the diagram below, AB ∥ CD. Determine the size of x, giving a reason.
(2)
x = 48° (corresp ∠s; AB ∥ CD)✓✓ (2)
3
In the diagram below, AB ∥ CD. Determine the size of x, giving a reason.
(2)
x = 180° − 130° = 50° (co-int ∠s; AB ∥ CD)✓✓ (2)
4
In the diagram below, AB ∥ CD. Determine the size of x, giving a reason.
(2)
x = 180° − 90° = 90° (co-int ∠s; AB ∥ CD)✓✓ (2)
5
In the diagram below, POQ is a straight line. Determine the size of x.
(2)
x = 180° − 72° = 108° (∠s on a str line)✓✓ (2)
6
Two straight lines intersect as shown in the diagram below. Determine the size of x.
(2)
x = 115° (vert opp ∠s)✓✓ (2)
7
In the diagram below, AB ∥ CD. Determine the sizes of y and then x, giving reasons.
(2)
y = 100° (corresp ∠s; AB ∥ CD), then x = 180° − 100° = 80° (co-int ∠s; AB ∥ CD)✓✓ (2)
8
In the diagram below, AB ∥ CD. Calculate the value of x.
(2)
3x + 60 = 180 → 3x = 120 → x = 40✓✓ (2)
9
In the diagram below, AB ∥ CD. Calculate the value of x.
(2)
4x = x + 45 → 3x = 45 → x = 15✓✓ (2)
10
In the diagram below, AB ∥ CD. Calculate the value of x.
(2)
5x − 20 = 3x + 10 → 2x = 30 → x = 15✓✓ (2)

TOTAL: 20 marks