Chapter 4.3, Problem 15PSC

To determine

To calculate: To find measure of two angles.

Answer to Problem 15PSC

  ${45}^{\circ }\text{and}{60}^{\circ }$

Explanation of Solution

Given information: Ratio of complement of two angles is 3:2 and ratio of their supplements is 9:8.

Formula used: Supplement of an angle $x^{\circ }$ is ${(180-x)}^{\circ }$ and complement is ${(90-x)}^{\circ }$ .

Calculation: let measure of the angles be $x^{\circ }$ and $y^{\circ }$ .

  $\begin{array}{l}Then\frac{90-x}{90-y}=\frac{3}{2}and\frac{180-x}{180-y}=\frac{9}{8}\\ \therefore 270-3y=180-2x\text{and}1620-9y=1440-8x\\ 2x-3y=-{90}^{\circ }\text{and}8x-9y=-{180}^{\circ }\\ \text{Solving}\text{these}\text{equations,}\text{we}\text{ge}t\\ x={45}^{\circ }andy={60}^{\circ }\end{array}$