Chapter 2.4, Problem 12PSB

To determine

To calculate: To find measure of complement of the angle.

Answer to Problem 12PSB

  ${40}^{\circ }$

Explanation of Solution

Given information: measure of supplement of an angle exceeds 3 times the measure of the complement of the angle by ${10}^{\circ }$ .

Calculation: let measure of the given angle is $x^{\circ }$

Its complement is ${(90-x)}^{\circ }$ and according to the given condition,

  $\begin{array}{l}$ {(180-x)}^{\circ }=3{(90-x)}^{\circ }+{10}^{\circ }$\therefore 180-x=270-3x+10\\ \because 2x={100}^{\circ }\\ \therefore x={50}^{\circ }\\ \therefore complement={90}^{\circ }-{50}^{\circ }\\ ={40}^{\circ }\end{array}$