Chapter 2, Problem 32RP

To determine

To find the measure of half of the complement

Answer to Problem 32RP

The measure of half of complement will be $\text{35}°$

Explanation of Solution

Given information :

The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20

Formula used :

Supplement of the angle $\text{x}°$ will be $\left(180-\text{x}\right)°$

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

Calculation :

Let angle be $\text{x}°$ , S be the supplement of the angle and C will be the complement of the angle, then

As per the question,

S = 2C+20

  $\begin{array}{l}\Rightarrow \left(180-\text{x}\right)=2\left(90-\text{x}\right)+20\\ \left(\because \text{S= 180}-\text{x and C = 90}-\text{x, by definition}\right)\\ \Rightarrow 2\text{x}-\text{x=180}-\text{180 +20}\\ \Rightarrow \text{x=20}\\ \therefore \text{The measure of half of complement}\\ \text{=}\frac{1}{2}\left(90-x\right)\\ =\frac{1}{2}\left(90-20\right)\\ =\frac{1}{2}\times 70\\ =35°\end{array}$