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11.05 Angles at a point

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.

Apply the idea

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 180-126Subtract 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.

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+150Add the given angles
\displaystyle =\displaystyle 260\degree
\displaystyle \text{Missing angle}\displaystyle =\displaystyle 360-260Subtract the sum from 360
\displaystyle =\displaystyle 100\degree
The image shows three angles that make up a revolution. Ask your teacher for more information.
Idea summary

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

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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