Chapter 2.4, Problem 5WE

To determine

Tofind:The measures of twocongruent complementary angles.

Answer to Problem 5WE

The measure of each of the two congruent complementary angles is 45.

Explanation of Solution

Given information:

The complementaryangles are congruent.

Conceptused:

Complementary angles are two angles that have a sum of 90°. The measure complementary angle of $\angle X$ is $m\left\{\text{comp }\angle X\right\}=\left(90-X\right)$ . Two angles are congruent if they have the same angle measure in degrees.

Calculations:

Let $\angle A$ and $\angle B$ are to congruent angles and complementary two each other. Then

  $\angle A\cong \angle B\Rightarrow m\angle A=m\angle B$$\angle A$ , and $\angle B$ are congruent

  $m\angle A+m\angle B=90$$\angle A$ , and $\angle B$ are complementary

  $\Rightarrow m\angle A+m\angle A=90$

  $\Rightarrow 2m\angle A=90$$\because m\angle A=m\angle B$

  $\Rightarrow m\angle A=\frac{90}{2}=45$

  $\Rightarrow m\angle B=45$$\because m\angle A=m\angle B$

Thus, the measure of each of the two congruent complementary angles is 45.

Conclusion:

The measure of each of the two congruent complementary angles is 45.