An angle is $\frac{2}{3}$ of its supplement. What is its magnitude?

Given :

An angle is $\frac{2}{3}$ of its supplement.

To do :

We have to find the magnitude of the angle.

Solution : 

Supplementary angles:

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

Let the measure of the supplementary angle be x.

This implies,

The measure of the given angle $= \frac{2}{3}(x)$.

Therefore,

$x +\frac{2}{3} x = 180°$

$\frac{(3+2)}{2} x = 180°$

$\frac{5}{3} x = 180°$

$5x = 3(180°)$

$5x = 540°$

$x = \frac{540°}{5}$

$x = 108°$

Therefore, the measures of the angles are 108° and $\frac{2}{3}(108)° = 2(36)° = 72°$.

The magnitude of the required angle is 72°.