# Basic angle rules

## In a nutshell

There are five rules involving angles on lines and shapes. These rules refer to angles in a triangle, angles on a straight line, angles in a quadrilateral, angles around a point and angles in an isosceles triangle. The rules help to find missing angles on lines and in shapes.

## Angles in a triangle

The angles in a triangle add up to $180\degree$.

**Example 1**

*Find the size of the missing angle in the triangle:*

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*Angles in a triangle add up to $180\degree$. *

*$\begin{aligned}70\degree+30\degree & =100\degree \\180\degree-100\degree &=80\degree\end{aligned}$ ** *

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

## Angles on a straight line

Angles on a straight line add up to $180\degree$.

**Example 2**

*Find the size of the missing angle on the straight line:*

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*Angles on a straight line add up to *$180\degree$*. *

*$180\degree - 100\degree = 80\degree$*

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

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## Angles in a quadrilateral

Angles in a quadrilateral add up to $360\degree$.

**Example 3**

*Find the size of the missing angle in the quadrilateral shown:*

*Angles in a quadrilateral add up to $360\degree$. Subtract the sum of the known angles from $360\degree$. *

*$\begin{aligned}80\degree+120\degree+40\degree &= 240\degree \\ 360\degree- 240\degree &= 120\degree\end{aligned}$*

*The missing angle is $\underline{120\degree}$.*

## Angles around a point

Angles around a point add up to $360\degree$.

**Example 4**

*Find the size of the missing angle:*

*Angles around a point add up to $360\degree$, so take $140\degree$ away from $360\degree$.*

*$360\degree- 140\degree= 220\degree$*

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

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## Angles in an isosceles triangle

Isosceles triangles have two sides equal in length and two equal angles. The two equal angles are sometimes referred to as the '*base angles*' in an isosceles triangle. If you know one of the angles in an isosceles triangle, the other two angles can be found easily.

**Example 5**

*The isosceles triangle has equal sides $AC$ and $BC$. If $\angle BAC$ is $50\degree$, find the size of $\angle ACB$.*

*$\angle BAC$ and $\angle ABC$ are both $50\degree$, as they are the base angles of the triangle. As angles in a triangle add up to $180\degree$, you can find $\angle ACB$ by subtracting the sum of $\angle ABC$ and $\angle BAC$ from $180\degree$.*

*$\begin{aligned}50\degree+50\degree &= 100\degree \\180\degree - 100\degree &= 80\degree\end{aligned}$*

*$\underline{\angle\ ACB\ = 80\degree}$*

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