Chapter 12.1, Problem 6E

To determine

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

Answer to Problem 6E

The measure of the angle that is complementary to an angle measuring ${45}^o$ is ${45}^o$ .

Explanation of Solution

Given: Two angles are a complementary angle pair and one of the angles measures ${45}^o$ .

Concept Used: If the sum of 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

  $m\angle 3+m\angle 4={90}^o$

  $\Rightarrow {45}^o+m\angle 4={90}^o$

  $\Rightarrow m\angle 4={90}^o-{45}^o={45}^o$$$

Therefore, the measure of the angle that is complementary to an angle measuring ${45}^o$ is $45^o$ .