Chapter 2.2, Problem 19PSB

To determine

To calculate: to find half the measure of larger angle.

Answer to Problem 19PSB

  ${27}^{\circ }$

Explanation of Solution

Given information: two complementary angles, such that one is added to half the other yields ${27}^{\circ }$ .

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

Calculation: let the angles be $x^{\circ }$ and $\begin{array}{l}x={90}^{\circ }-{36}^{\circ }={54}^{\circ }\\ \therefore \frac{x}{2}={27}^{\circ }\end{array}$

Then according to given condition,

  $x+\frac{1}{2}y={72}^{\circ }\mathrm{....}(1)$

  $\because$ These angles are complementary,

  $\therefore x+y={90}^{\circ }\mathrm{....}(2)$

Subtracting equation (1) from (2) .

  $\begin{array}{l}\frac{1}{2}y={18}^{\circ }\\ \therefore y={36}^{\circ }\end{array}$

Consequently,

  $\begin{array}{l}x={90}^{\circ }-{36}^{\circ }={54}^{\circ }\\ \therefore \frac{x}{2}={27}^{\circ }\end{array}$