# The measure of a complement is 1/4 of the measure of its angle. How do you find the angle measure?

Nov 16, 2017

72

#### Explanation:

An angle's complement, when added to the angle itself, sums to 90 degrees ($\frac{\pi}{2}$ radians).

So you have

$x + \frac{1}{4} x = 90$

$\frac{4}{4} x + \frac{1}{4} x = 90$

$\frac{5}{4} x = 90$

$x = 90 \cdot \frac{4}{5} = \frac{360}{5} = 72$