The two angles should add up to 180\degree since they lie on a straight line. So to find the missing angle we can subtract 129\degree from 180\degree .

\displaystyle \text{Missing angle}	\displaystyle =	\displaystyle 180-126	Subtract 126 from 180
	\displaystyle =	\displaystyle 54\degree

Idea summary

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

Angles at a point

This video looks at angles at a point, and how to use a full revolution being equal to 360 degrees to answer problems.

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Examples

Example 2

Find the size of the missing angle.

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

Worked Solution

Create a strategy

Add the given angles and subtract the sum from 360\degree, which is the angle in a revolution.

Apply the idea

The three angles should add to 360\degree since they make up a revolution. So if we add up the given angles and subtract them from 360\degree , we will find the unknown angle.

\displaystyle \text{Sum}	\displaystyle =	\displaystyle 110+150	Add the given angles
	\displaystyle =	\displaystyle 260\degree

\displaystyle \text{Missing angle}	\displaystyle =	\displaystyle 360-260	Subtract the sum from 360
	\displaystyle =	\displaystyle 100\degree

Idea summary

It doesn't matter how many angles are formed at a point, the sum is always 360 degrees.

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

12.05 Angles at a point

Ideas

Are you ready?

Examples

Example 1

Angles at a point

Examples

Example 2

Outcomes

AC9M6M04

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