Chapter 9, Problem 14CR

To determine

To find:The complement of the angle.

Answer to Problem 14CR

The complement of the angle is ${10}^0$

Explanation of Solution

Given information:The following statement has been given

The sum of an angle and four times it’s complement is ${20}^0$ greater that the supplement of the angle.

Calculation:We assume the unknown angle to be x . hence, we can infer the following equation from the given statement

  $\begin{array}{l}x+4({90}^0-x)={20}^0+({180}^0-x)\\ x+{360}^o-4x={20}^o+{180}^o-x\\ 2x={160}^o\\ x={80}^o\end{array}$

Hence, from the given equation, we can say that

  $x={80}^0$

Now, for the complement, we say

  $\begin{array}{l}={90}^0-x\\ ={90}^0-{80}^0\\ ={10}^0\end{array}$