Chapter 2.4, Problem 17PSB

To determine

To calculate: To find supplement of the angle.

Answer to Problem 17PSB

  ${165}^{\circ }$

Explanation of Solution

Given information: Three times the supplement of an angle is subtracted from seven times the complement; the answer is same as trisecting right angle.

Calculation: let measure of the angle be $x^{\circ }$ then its supplement in ${(180-x)}^{\circ }$ and its complement is ${(90-x)}^{\circ }$ .

According to the question,

  $\begin{array}{l}$ 7{(90-x)}^{\circ }-3{(180-x)}^{\circ }=\frac{1}{3}\times {90}^{\circ }$\therefore 630-7x-540+34={30}^{\circ }\\ \Rightarrow {60}^{\circ }\\ \therefore x={15}^{\circ }\end{array}$

Hence supplement

  $\begin{array}{l}$ ={(180-15)}^{\circ }$={165}^{\circ }\end{array}$