Question

In the diagram,$\angle \mathit{A}\mathit{F}\mathit{B}$ is a right angle. Name the figures described.

Two congruent supplementary angles.

Short answer

The two congruent supplementary angles are$\angle \mathit{A}\mathit{F}\mathit{B}$and $\angle \mathit{A}\mathit{F}\mathit{D}$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

From the given diagram it can be noticed that:

$\angle AFB=90°$

Step 2. Definition of congruent and supplementary angles.

The supplementary angles are the angles whose sum is $\mathbf{180}\mathbf{°}$.

The congruent angles are the angles which have same measure.

Step 3. Description of step.

From the given diagram it can be noticed that the angles$AFB$ and$AFD$ forms the linear pair as they are lying on the straight line.

Therefore, the sum of the angles$AFB$ and$AFD$ is $180°$.

That implies $\angle AFB+\angle AFD=180°$.

Therefore, the angles$AFB$ and$AFD$ are the supplementary angles.

Step 4. Description of step.

Find the value of the angle$AFD$ by using the fact that $\angle AFB+\angle AFD=180°$.

$$\begin{gathered} \angle AFB+\angle AFD=180° \\ 90°+\angle AFD=180° \\ \angle AFD=180°-90° \\ \angle AFD=90° \end{gathered}$$

Therefore, the measure of the angle$AFD$ is $90°$.

Therefore, $\angle AFB=\angle AFD=90°$.

Therefore, the angles$AFB$ and$AFD$ are the congruent angles.

Step 5. Write the name of the two congruent supplementary angles.

The angles$AFB$ and$AFD$ are congruent angles as well as they are supplementary angles.

Therefore, the name of the two congruent supplementary angles is$AFB$ and $AFD$.