Chapter 2.2, Problem 5PSA

To determine

To calculate: measure of two complementary angles satisfying the given condition.

Answer to Problem 5PSA

  ${30}^{\circ }$ And ${60}^{\circ }$

Explanation of Solution

Given information: out of two complementary angles, one angle is twice the other.

Formula Used: sum of complimentary angles is ${90}^{\circ }$ .

Calculation: let measure of smaller angle be $x^{\circ }$ , then greater angle has measure $2x^{\circ }$ .

  $\because$ These angles are complementary.

  $\begin{array}{l}\therefore x^{\circ }+2x^{\circ }={90}^{\circ }\\ \therefore 3x^{\circ }={90}^{\circ }\end{array}$

  $\therefore x^{\circ }={30}^{\circ }$ And $2x^{\circ }={60}^{\circ }$ .