# Two angles are supplementary. One angle is 5 degrees less than four times the other. What are the measures of the angles?

May 28, 2018

$a = {143}^{o}$, $b = {37}^{o}$

#### Explanation:

To be able to answer this, we must know what it means that the angles are supplementary. If you have two angles a and b and
$a + b = {180}^{o}$, they are supplementary.

As $a = 4 b - {5}^{o}$,
$a + b = 4 b - {5}^{o} + b = 5 b - {5}^{o} = {180}^{o}$
which gives $b = {185}^{o} / 5 = {37}^{o}$
Therefore $a = {180}^{o} - b = {143}^{o}$

May 28, 2018

$\textcolor{b l u e}{{143}^{\circ} , {37}^{\circ}}$

#### Explanation:

Let the angle be $\theta$

One angle is 5 degrees less than four times the other.

One angle is $4 \theta - 5$

The other angle is $\theta$

Supplementary implies:

$4 \theta - 5 + \theta = 180 \implies \theta = 37$

So the angles are:

$4 \left(37\right) - 5 = {143}^{\circ}$

${37}^{\circ}$