Question

If an angle is $\frac{1}{4}$ of its supplement,then the degree measure of the angle is

• A. $36°$
• B. $45°$
• C. $144°$
• D. $135°$

Answer 1

The correct option is A

$36°$

Find the angle.

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

Let the angles be $x,\frac{x}{4}$.Then,

$\begin{array}{rcl}x+\frac{x}{4}& =& 180°\\ \frac{5x}{4}& =& 180°\\ 5x& =& 180°\times 4\\ x& =& (180°\times 4)÷5\\ x& =& 144°\\ \frac{x}{4}& =& 36°\end{array}$

Hence, the measure of angle is $\mathbf{36}\mathbf{°}$

Thus the correct answer is option A.