Question

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

Two complementary angles.

Short answer

The two complementary angles are$\angle \mathit{A}\mathit{F}\mathit{E}$and $\angle \mathit{E}\mathit{F}\mathit{D}$.

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 complementary angles.

The complementary angles are the angles whose sum is $\mathbf{90}\mathbf{°}$.

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 $\angle AFB+\angle AFD=180°$.

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 $90°$.

Step 5. Find the sum of the angles AFE and EFD.

From the given diagram it can be noticed that:

$\angle AFD=\angle AFE+\angle EFD$.

Therefore,

$$\begin{gathered} \angle AFD=\angle AFE+\angle EFD \\ 90°=\angle AFE+\angle EFD \end{gathered}$$

Therefore, the sum of the angles$AFE$ and$EFD$ is $90°$.

Step 6. Write the name of the two complementary angles.

As, thesum of the angles$AFE$ and$EFD$ is $90°$.

Therefore, the angles$AFE$ and$EFD$ are complementary angles.

Therefore, the name of the two complementary angles is$\angle AFE$ and $\angle EFD$.