Chapter 8.1, Problem 17PSB

To determine

To calculate: The measure of the supplement of given angle.

Answer to Problem 17PSB

The measure of the supplement of given angle is $150°$

Explanation of Solution

Given information The ratio of the measure of the supplement of an angle to the measure of the complement of the angle is $5:2$

Formula used Supplement of angle A is 180 − A and

Complement of angle A is 90 − A

Calculation Let us assume that angle be A

Then supplement of the angle will be $\left(180-\text{A}\right)°$ and

Complement of the angle will be $\left(90-\text{A}\right)°$

Since, ratio is given as

  $\begin{array}{l}\left(180\text{-A}\right):\left(90-\text{A}\right)=5\text{A}-2\text{A}\\ \therefore \text{ 180}-\text{A=5A}\\ \Rightarrow \text{5A+A=180}\\ \Rightarrow \text{6A=180}\\ \Rightarrow \text{A=30}\end{array}$

Thus, supplement of the angle

  $\begin{array}{l}=180°-\text{A}°\\ =180°-30°\\ =150°\end{array}$