Angles around a point and on a straight line

In a nutshell

Angles on a straight line add up to $180\degree$ and angles around a point add up to $360\degree$ . You can use this knowledge to work out missing angles.

Angles on a straight line

Angles on a straight line add up to $180\degree$ . One way to see this is to look at two right angles lined up side by side.

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

A right-angle is an angle that is exactly $90\degree$ . When two right angles are lined up together, a straight line is formed. Therefore, angles on a straight line add up to $180\degree$ because $90 + 90 = 180$ .

Example 1

Find the missing angle.

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

The angle given is $100\degree$ . Angles on a straight line add up to $180\degree$ , so the missing angle can be worked out by:

$180 - 100 = 80$

The missing angle is $\underline{80\degree}$ .

Angles around a point

Angles around a point add up to $360\degree$ . Right-angles can be used to prove this again.

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

As right-angles are angles which are exactly $90\degree$ , angles around a point must be $90 + 90 + 90 + 90 = 360\degree$ .

Example 2

Find the missing angle.

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

The angle given is $140\degree$ . Angles around a point add up to $360\degree$ .

Therefore, the missing angle can be worked out by:

$360-140=220$ 

The angle is $\underline{220\degree}$ .

Vertically opposite angles

When two lines intersect, they create a cross. When this happens, the opposite angles they create are equal.

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

In the case of this diagram, due to the cross these lines create, the angles A and B are equal.

Example 3

If angle $A$  is $60\degree$ , work out angle $B$ .

Maths; Geometry - properties of shapes; KS2 Year 5; Angles around a point and on a straight line

Angles that are vertically opposite are equal, so angle A = C = $60\degree$ .

This means that:

$A + C = 120\degree$

Angles around a point add up to $360\degree$ . This means that:

$B + D = 360 - 120 = 240$

B and D are opposite, and therefore equal, so:

$B = \dfrac{240}{2} = 120$

$B=\underline{120\degree}$