# The measure of the supplement of an angle is three times the measure of the complement of the angle. How do you find the measures of the angles?

Aug 22, 2017

Both angles are ${45}^{\circ}$

#### Explanation:

$m + n = 90$
as an angle and its complement equal 90

$m + 3 n = 180$

as an angle and its supplement equals 180

Subtracting both equations will eliminate m

$m + 3 n - m - n = 180 - 90$ this gives

$2 n = 90$ and dividing both sides by $2$ gives

$2 \frac{n}{2} = \frac{90}{2}$ so

$n = 45$

substituting $45$ for $n$ gives

$m + 45 = 90$ subtracting $45$ from both sides gives.

$m + 45 - 45 = 90 - 45$ so

$m = 45$

Both the angle and it complement are $45$

The supplement is $3 \times 45 = 135$