Two supplementary angles are in the ratio $4 : 5$. Find the angles.

Given:

Two supplementary angles are in the ratio $4 : 5$.

To do:

We have to find the measure of the angles.

Solution:

Two angles are said to be supplementary if the sum of their measures is $180^o$.

Let the required angles be $4x$ and $5x$.

Therefore,

$4x+5x=180^o$

$9x=180^o$

$x=\frac{180^o}{9}$

$x=20^o$

This implies,

$4x=4(20^o)=80^o$

$5x=5(20^o)=100^o$

The measures of the required angles are $80^o$ and $100^o$.