Angles are all around us, and though we may not realise it, even opening a door creates an angle! Understanding what an angle is means we are now able to solve problems where we may need to add two angles together, or use subtraction to find the value of a missing angle.

In Video 1, we work through some examples where we need to add angles, then an example where we subtract angles.

Your turn to add angles

Why don't you use this applet to add some angles together. You can also change the size of one or both angles, and then press add to see what happens when you add them together.

Created with Geogebra

Did you see that the two smaller angles add to the size of the larger angle?
What are the two largest angles you can select, using this applet?
Why weren't you able to select larger angles?

Let's subtract angles

In this second applet, you can select two or more angles, and subtract one from the other, to see the resulting angle.

Created with Geogebra

Remember!

Naming angles follows a set of rules. We use capital letters to label each point, and the vertex, where adjacent lines meet, is always the middle letter. For this diagram below, you could label this as $\angle RST$∠RST or $\angle TSR$∠TSR.

Worked Examples

Question 1

Calculate the size of $\angle ABC$∠ABC.

Question 2

$Eileen$ is practising her pirouettes for ballet class.

The first time she tries, she spins $121^\circ$121°. After $2$2 weeks practice, she can spin $238^\circ$238°.

How many degrees further can she spin now?

Question 3

Find $x$x in the figure below.

Addition and subtraction problems involving angles

Working with angles