Primary 5 maths · Geometry · About 12 minutes
Use vertically opposite angles
Locate the common vertex, the given lines and the complete turn being filled.
Start the interactive lesson →Open practice activity
What you will learn
- Use vertically opposite angles
Models used: number sentences, stories, tables.
Before you start
Two ways to finish the same straight turn
The blue angle is 60°. The adjacent orange angle must be 120° to make a straight turn.
The straight line is the whole half-turn. The coloured arcs show its two parts.
The blue angle is 60°. The adjacent orange angle must be 120° to make a straight turn.
60° + 120° = 180°
A straight turn, a full turn and vertically opposite angles use different facts. The markings decide which fact applies.
Angles directly across the crossing are opposite angles. Angles side by side complete a straight turn.
The angle across the crossing shares that same 120° neighbour. It must also be 60°.
180° − 120° = 60°
The straight line is the whole half-turn. The coloured arcs show its two parts.
That is why vertically opposite angles match: each completes a straight turn with the same neighbour.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
What did the picture help us see?
That is why vertically opposite angles match: each completes a straight turn with the same neighbour.
Worked example: A new example, together
Two straight lines cross. One angle is 90°. Find the vertically opposite angle.
| Known angle | Relationship |
|---|---|
| 90° | opposite at an intersection |
Use the marked relationship. Read each value with the heading above its column.
Locate the common vertex, the given lines and the complete turn being filled.
Two intersecting straight lines create equal vertically opposite angles.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
Vertically opposite angles are equal.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Two straight lines cross. One angle is 90°. Find the vertically opposite angle.
90 degrees
Use the marked relationship. Read each value with the heading above its column.
Vertically opposite angles are equal.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
The angle across the vertex matches 90°.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
x = 90°.
Use the marked relationship Known angle Relationship 90° opposite at an intersection Use the marked relationship. Read each value with the heading above its column.
Check the result against the question we started with.
The opposite angle equals 90°.
We found 90 degrees. Two intersecting straight lines create equal vertically opposite angles.
Use the marked relationship Known angle Relationship 90° opposite at an intersection
Common mistakes to discuss
- Opposite angles add to 180°. Vertically opposite angles are equal. Where lines cross, the angle opposite 40° is also 40°; it is the neighbouring angle that makes 180°.
Check your understanding
- Use vertically opposite angles
- justify an unknown angle with the stated angle relationship
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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