11.08 Vertically opposite angles

Lesson

Ideas

Can you work out the value of an  angle on a straight line  ?

Examples

Example 1

Find the size of the missing angle.

Worked Solution
Create a strategy

Subtract the given angle from 180\degree, which is the angle in a straight line.

Apply the idea
Idea summary

Angles on a straight line always add up to 180 degrees.

Vertically opposite angles

This video shows you how supplementary angles can help us understand that vertically opposite angles are always equal and then how to use vertically opposite angles to answer questions.

Examples

Example 2

Find the size of the missing angle.

Worked Solution
Create a strategy

Find the vertically opposite angles and use the fact that they are equal.

Apply the idea

The missing angle and the 35 \degree angle make an angle that is vertically opposite to the 119\degree angle. That means these angles are equal.

So to find the missing angle we can subtract 35 \degree from 119\degree .

Idea summary

Vertically opposite angles are always equal. 'Vertically opposite' means they are opposite in relation to the vertex, not up and down.

Outcomes

MA3-16MG

measures and constructs angles, and applies angle relationships to find unknown angles