Topics
11. Geometry
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AustraliaVIC
Level 6

11.06 Vertically opposite angles

Lesson
Practice
Lesson

Are you ready?

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

Examples

Example 1

Find the size of the missing angle.

The image shows two angles that make up a straight angle. Ask your teacher for more information.
Worked Solution
Create a strategy

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

Apply the idea
\displaystyle \text{Missing angle}\displaystyle =\displaystyle 180-126Subtract 126 from 180
\displaystyle =\displaystyle 54\degree
The image shows two angles that make up a straight angle. Ask your teacher for more information.
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.

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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 119-35Subtract 35 from 119
\displaystyle =\displaystyle 84\degree
The image shows angles that make up a revolution including vertically opposite angles. Ask your teacher for more information.
Idea summary

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

Outcomes

VCMMG231

Investigate with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles.

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