Chapter 2.4, Problem 6WE

To determine

Tofind:The measures of twocongruent supplementary angles.

Answer to Problem 6WE

The measure of each of the two congruent supplementary angle is 90.

Explanation of Solution

Given information:

The complementaryangles are congruent.

Conceptused:

Supplementary angles are two angles that have a sum of 180°. The measure of a supplementary angle of $\angle Z$ is $m\left\{\sup \angle Z\right\}=180-Z$ .

Calculations:

Let $\angle A$ and $\angle B$ are to congruent angles and supplementary 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=180$$\angle A$ , and $\angle B$ are complementary

  $\Rightarrow m\angle A+m\angle A=180$

  $\Rightarrow 2m\angle A=180$$\because m\angle A=m\angle B$

  $\Rightarrow m\angle A=\frac{180}{2}=90$

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

Thus, the measure of each of the two congruent complementary angle is 90.

Conclusion:

The measure of each of the two congruent complementary angle is 90.