Chapter 10, Problem 1T

If an angle measures ${54}^{\circ }$, find the measure of its complement and supplement.

To determine

To calculate: The measure of complement and supplement of 54 degrees.

Answer to Problem 1T

Solution: The measure of supplement angle is ${36}^{\circ }$ and the measure of compliment angle is ${126}^{\circ }$.

Explanation of Solution

Given: The angle whose measure is ${54}^{\circ }$.

Formulae used:

$\begin{array}{l}\text{Measure of the complement}={90}^{\circ }-\theta ,\\ \text{Measure of the complement}={180}^{\circ }-\theta \end{array}$

Calculation: The measure of the complement can be obtained by subtracting the measure of the angle from the ${90}^{\circ }$. by using formula

$\begin{array}{c}\text{Measure of the complement}={90}^{\circ }-{54}^{\circ }\\ ={36}^{\circ }\end{array}$

The measure of the supplement angle can be obtained by subtracting the measure of the angle from the ${180}^{\circ }$. By using formula;

$\begin{array}{c}\text{Measure of the complement}={180}^{\circ }-{54}^{\circ }\\ ={126}^{\circ }\end{array}$

Hence, the measure of supplement angle is ${36}^{\circ }$ and the measure of compliment angle is ${126}^{\circ }$.