Chapter 12.1, Problem 5C

To determine

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

Answer to Problem 5C

The measure of the angle that is complementary to an angle measuring ${24}^o$ is ${66}^o$ .

Explanation of Solution

Given Information: Two angles are a supplementary angle pair and the measure of one of the angles is ${45}^o$ .

Concept Used: If the sum measures of two 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 $\angle 3$ and $\angle 4$ are complementary angles

  $m\angle 3+m\angle 4={90}^o$

  $\Rightarrow {24}^o+m\angle 4={90}^o$

  $\Rightarrow m\angle 4={90}^o-{24}^o={66}^o$$$

Therefore, the measure of the angle that is complementary to an angle measuring ${24}^o$ is $66^o$ .