91Ó°ÊÓ

The given diagram is:

From the given diagram it can be noticed that:

$∠AFB=90°$

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

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 $∠AFB+∠AFD=180°$.

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

$$\begin{gathered} ∠AFB+∠AFD=180° \\ 90°+∠AFD=180° \\ ∠AFD=180°−90° \\ ∠AFD=90° \end{gathered}$$

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

From the given diagram it can be noticed that:

$∠AFD=∠AFE+∠EFD$.

Therefore,

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

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

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$∠AFE$ and $∠EFD$.