Question

Two supplementary angles are congruent. Find their measures.

Short answer

The measures of two supplementary angles that are congruent are 90 and 90.

Step-by-step solution

Step 1. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180.

Step 2. Definition of congruent angles.

The two angles are said to be congruent angles if they have equal measure.

Step 3. Write the relations between the angles A and B.

Consider the two supplementary angles that are congruent be$\angle A$ and $\angle B$.

As the angles$\angle A$ and$\angle B$ are supplementary angles.

Therefore,

$\angle A+\angle B=180\left(1\right)$.

As the angles$\angle A$ and$\angle B$ are congruent angles.

Therefore,

$\angle A=\angle B\left(2\right)$

Step 4. Solve the equations (1) and (2) by substituting A for B into the equation (1).

$$\begin{gathered} \angle A+\angle B=180 \\ \angle A+\angle A=180 \\ 2\angle A=180 \\ \angle A=\frac{180}{2} \\ \angle A=90 \end{gathered}$$

Therefore, the value of the angle$\angle A$ is 90.

Step 5. Find the value of B.

$\begin{array}{c}\angle B=\angle A\\ =90\end{array}$

Therefore, the value of the angle$\angle B$ is 90.

Step 6. Write the measures of the two supplementary angles that are congruent.

The measures of the two supplementary angles that are congruent are 90 and 90.