Chapter 2.4, Problem 31WE

To determine

The measures of the angle, its supplement, and its complement.

Answer to Problem 31WE

The measure of the angle is ${72}^{\circ }$

The measure of its supplement is ${108}^{\circ }$

The measure of its complement is ${18}^{\circ }$

Explanation of Solution

Given information:

A supplement of an angle is six times as large as a complement of the angle.

Suppose the measure of the angle be $x$

Then the measure of its supplement is $180-x$

Then the measure of its complement is $90-x$

The measure of the supplement of the angle is 6 times as large as a complement of the angle

  $180-x=6(90-x)$

Simplifying this gives

  $\begin{array}{l}\begin{array}{l}180-x=6(90-x)\\ 180-x=540-6x\end{array}\hfill \\ \begin{array}{l}5x={360}^{\circ }\\ x={72}^{\circ }\end{array}\hfill \end{array}$

Thus, the measure of the angle is ${72}^{\circ }$

Then the measure of its supplement is

  $\begin{array}{l}180-x={180}^{\circ }-{72}^{\circ }\\ ={108}^{\circ }\end{array}$

Then the measure of its complement is

  $\begin{array}{l}90-x={90}^{\circ }-{72}^{\circ }\\ ={18}^{\circ }\end{array}$