# 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.

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.*

*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.

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.*

*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.

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 *$B$.

**

*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:*

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

$B=\underline{120\degree}$