Chapter 2.4, Problem 30WE

To determine

The measure of an angle and its supplement

Answer to Problem 30WE

Thus, the measure of the angle is ${84}^{\circ }$

And, the measure of the supplement is ${96}^{\circ }$

Explanation of Solution

Given information:

The measure of a supplement of an angle is 12 more than twice the measure of the angle.

Suppose the measure of the angle be $x$

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

The measure of the supplement of the angle is 12 more than the angle implies that

  $180-x=12+x$

Simplifying this gives

  $\begin{array}{l}180-x=12+x\hfill \\ 168=2x\hfill \end{array}$

  $x={84}^{\circ }$

And

  $\begin{array}{l}180-x={180}^{\circ }-{84}^{\circ }\\ ={96}^{\circ }\end{array}$

Thus, the measure of the angle is ${84}^{\circ }$

And, the measure of the supplement is ${96}^{\circ }$