Chapter 12.1, Problem 23E

To determine

To Calculate: The other angle of a complementary angle pair when one angle is given.

Answer to Problem 23E

The measure of the angle that is complementary to an angle measuring ${81}^o$ is $9^o$ .

Explanation of Solution

Given Information: Two angles are a complementary angle pair and the measure of one of the angles is $9^o$ .

Concept Used: If the sum of measures oftwo angles is ${90}^o$ then the angles are called complementary angles and if the sum is ${180}^o$ then the angles are called supplementary angles.

Calculation: Since $\angle 1$ and $\angle 2$ are complementary angles

  $m\angle 1+m\angle 2={90}^o$

  $\Rightarrow {81}^o+m\angle 2={90}^o$

  $\Rightarrow m\angle 2={90}^o-{81}^o=9^o$$$

Therefore, the measure of the angle that is complementary to an angle measuring ${81}^o$ is $9^o$ .