Chapter 2.2, Problem 21PSB

To determine

To calculate: find measure of complement of the angle.

Answer to Problem 21PSB

  ${30}^{\circ }$

Explanation of Solution

Given information: supplement of an angle is four times its complement

Formula Used: sum of two supplementary angles is ${180}^{\circ }$ .

Calculation: let measure of the angle be $x^{\circ }$ .

Then its supplement is $$ and complement is ${(90-x)}^{\circ }$ . According to the given condition.

  $\begin{array}{l}$ {(180-x)}^{\circ }=4{(90-x)}^{\circ }$\therefore 180-x=360-4x\\ \therefore 3x=180\\ \therefore x={60}^{\circ }\end{array}$

Hence its complement is ${30}^{\circ }$ . $({90}^{\circ }-{60}^{\circ }={30}^{\circ })$