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A full turn through a point is 360°. Angles around a point always add up to 360°.

If you know one of the angles, you will be able to work out other angles around the point. You don’t always need a protractor.

What is the value of A?

These two angles are around a point. They must add up to 360°.

135° + A = 360°

We can rearrange this to find angle A:

A = 360° - 135°

Therefore:

360° - 135° = 225°

Angle A is 225°.

However, sometimes you need to find more than one angle around a point.

What is the value of angle B?

What can you see on this diagram? 168°, angle B and a small square.

We typically represent a right angle with a small square. A right angle is always 90°.

As before, all these angles together must equal 360°.

B + 90° + 168° = 360°

First add together the angles we know the value of:

90° + 168° = 258°

Then subtract this from 360° to find the missing angle.

360° - 258° = 102°

Therefore, angle B is 102°.

This diagram shows that there are two angles to be found.

What are angles C and D?

The angles either side of the straight line must add up to 180°.

To find angle C, you can subtract 112° from 180°.

180° - 112° = 68°

Angle C is 68°.

To find angle D, subtract 145° from 180°.

180° - 145° = 35°

Angle D is 35°.

Try this quiz to see how well you know the topic!

The hands of a clock are pointing at 12 and 9.

Can you calculate the angle between the two hands?

You could even draw your own clock to help you solve this problem.

Now, taking what you have learned from the guide, work out the outside angle of the clock hands based on your answer above.

Do both answers add up to 360°?