The measure of an angle is five less than four times the measure of its supplement. How do you find both angle measures?

1 Answer
Oct 21, 2016

The angle measures ${143}^{o}$ and the supplementary angle measures ${37}^{o}$.

Explanation:

Consider the angle as $L$ and the supplement, by definition, will be $\left(180 - L\right)$

According to the problem above:

$L = 4 \left(180 - L\right) - 5$

Open the brackets.

$L = 720 - 4 L - 5$

Simplify the equation.

$L = 715 - 4 L$

Add $4 L$ to both sides.

$5 L = 715$

Divide both sides by $5$.

$L = 143$

Consequently, the supplementary angle is:

$180 - L = 180 - 143 = 37$.