Chapter 2.4, Problem 29WE

To determine

The measure of an angle that is half as large as its complement

Answer to Problem 29WE

The measure of the angle is ${30}^{\circ }$

Explanation of Solution

Given information:

An angle that is half as large as its complement

Suppose the measure of the angle be $x$

Then the measure of its complement is $180-x$

The measure of the angle is twice as large as its complement implies that

  $x=\frac{1}{2}(90-x)$

Simplifying this gives

  $\begin{array}{l}x=\frac{1}{2}(90-x)\hfill \\ x={45}^{\circ }-\frac{x}{2}\hfill \end{array}$

  $\frac{3x}{2}={45}^{\circ }$

  $x={30}^{\circ }$

Thus, the measure of the angle is ${30}^{\circ }$