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11.05 Measure angles


Are you ready?

Can you  estimate the size  of an angle? This can be useful skill when checking our measurements are reasonable.


Example 1

Estimate the size of the angle made by the mountains at the centre.

This image shows a sunset. Ask your teacher for more information.
Greater than 90\degree
Less than 45\degree
Equal to 180\degree
Worked Solution
Create a strategy

Draw straight lines along the mountains to form an angle.

Apply the idea

Look at the angle marked by the arrows.

This image shows a sunset with the angle marked. Ask your teacher for more information.

The angle formed is obtuse, or greater than a 90\degree right angle. But it is not a straight angle so it is not 180\degree.

So the answer is option A: Greater than 90\degree.

Idea summary

If we remember some important angles, we can use those to estimate other angles.

Measure angles with a protractor

This video shows you how to use a protractor to measure acute, obtuse, and reflex angles.

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Example 2

What is the angle being measured by this protractor?

This image shows a protractor with an angle of 160 degrees marked on it. Ask your teacher for more information.
Worked Solution
Create a strategy

Look at the numbers that the lines go through.

Apply the idea

The horizontal line goes through the numbers 0 and 180. Since 0 is on the inside, we should use the inside number on the other line to measure the angle.

The other line goes through 160 and 20. But since 160 is on the inside, then the size of the angle is 160 \degree.

Idea summary

The protractor has two sets of numbers, make sure you are reading off the value of the angle from the correct set.

An image of a protractor.

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