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# An angle is $ \frac{1}{5} $ of its supplement. What is the degree measure of the angle?

Given :

An angle is $\frac{1}{5}$ of its supplement.

To do :

We have to find the degree measure of the angle.

Solution :

Supplementary angles:

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

Let the measure of the supplementary angle be $x$.

This implies,

The measure of the given angle $= \frac{1}{5}(x)$.

Therefore,

$x +\frac{1}{5} x = 180^o$

$\frac{(5+1)}{5} x = 180^o$

$\frac{6}{5} x = 180^o$

$6x = 5(180^o)$

$6x = 900^o$

$x = \frac{900^o}{6}$

$x = 150^o$

Therefore, the measures of the angles are $150^o$ and $\frac{1}{5}(150)^o = 30^o$.

The measure of the required angle is $30^o$.

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