Chapter 8, Problem 1IR

To determine

The supplement and complement of $27°$ .

Answer to Problem 1IR

The supplement of $27°$ is $153°$ and complement of $27°$ is $63°$ .

Explanation of Solution

Given:

The given angle is $27°$ .

Calculation:

Two angles are known to be supplementary angles when their sum is 180 degrees as shown below,

  $\angle A+\angle B=180°$

Here one of the measure of the angle is $\angle A=27°$ .

Substitute in above equation to find the supplementary of $\angle A$ .

  $\begin{array}{c}\angle A+\angle B=180°\\ 27°+\angle B=180°\\ \angle B=180°-27°\\ \angle B=153°\end{array}$

Thus, supplement of angle $27°$ is $153°$ .

Two angles are known to be complementary angles when their sum is 90 degrees as shown below,

  $\angle A+\angle B=90°$

Here one of the measure of the angle is $\angle A=27°$ .

Substitute in above equation to find the complementary of $\angle A$ .

  $\begin{array}{c}\angle A+\angle B=90°\\ 27°+\angle B=9°\\ \angle B=90°-27°\\ \angle B=63°\end{array}$

Thus, complement of angle $27°$ is $63°$ .

Conclusion:

The supplement of $27°$ is $153°$ and complement of $27°$ is $63°$ .