Chapter 6, Problem 18CR

To determine

To calculate: Measure of half of supplement.

Answer to Problem 18CR

Measure of half of supplement is $19.5°$ .

Explanation of Solution

Given information : Here, we have given that supplement of an angle exceeds three times the measure of its complement by $12$ .

Formula used : Complement angles are the angles whose sum is $90°$ and Supplement angles are the angles whose sum is $180°$

Calculation: Let the angle be $x$ .

  $\therefore$ Supplement = $(180-x)°$ and complement = $(90-x)°$

Now, according to the question,

  $\begin{array}{l}\Rightarrow (180-x)°-3(90-x)°=12\\ \Rightarrow 180°-x-270°+3x=12\\ \Rightarrow 2x-90°=12\\ \Rightarrow 2x=(12+90)°\\ \Rightarrow 2x=102°\\ \Rightarrow x=\frac{102°}{2}\\ \Rightarrow x=51°\end{array}$

  $\therefore$ Half of supplement of angle = $\frac{1}{2}(90-x)°$

  $\begin{array}{l}\Rightarrow \frac{1}{2}(90-51)°\\ \Rightarrow \frac{1}{2}\times 39°\\ \Rightarrow 19.5°\end{array}$