Chapter 9, Problem 2CUR

To determine

To find: the measure of an angle if the measures of a supplement and a complement of the angle have the ratio $5:2$ .

Answer to Problem 2CUR

The measure of the angle is $30°$ .

Explanation of Solution

Given information:

Calculation:

Suppose the angle is $x$ . Then the supplementary of this angle is $180-x$ and the complementary of the angle is $90-x$ .

Therefore from the given,

  $\begin{array}{c}\frac{180-x}{90-x}=\frac{5}{2}\\ 360-2x=450-5x\\ 3x=90\\ x=30\end{array}$

Hence, the measure of the angle is $30°$ .