# What is the ratio of the measure of the complement of a 50 degrees-angle to the measure of the supplement of the same angle?

Jun 15, 2015

$\left(\text{complement "50^@)/("supplement } {50}^{\circ}\right) = \frac{4}{13}$

#### Explanation:

By definition the complement of an angle is ${90}^{\circ}$ minus the angle
and the supplement of an angle is ${180}^{\circ}$ minus the angle.

The complement of ${50}^{\circ}$ is ${40}^{\circ}$
The supplement of ${50}^{\circ}$ is ${130}^{\circ}$

The ratio $\left(\text{complement "50^@)/("supplement } {50}^{\circ}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{{40}^{\circ}}{{130}^{\circ}} = \frac{4}{13}$