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.

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Examples

Example 2

Find the size of the missing angle.

The image shows angles that make up a revolution including vertically opposite angles. Ask your teacher for more information.

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 .

\displaystyle \text{Missing angle}	\displaystyle =	\displaystyle 119-35	Subtract 35 from 119
	\displaystyle =	\displaystyle 84\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

AC9M6M04

identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning

12.06 Vertically opposite angles

Ideas

Are you ready?

Examples

Example 1

Vertically opposite angles

Examples

Example 2

Outcomes

AC9M6M04

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