Question

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

Two non-congruent supplementary angles.

Short answer

The two non-congruent supplementary angles are$\angle \mathit{B}\mathit{F}\mathit{E}$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 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.

- Write relation between the angles BFE and EFD.

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

Therefore, the sum of the angles$BFE$ and$EFD$ is $180°$.

That implies $\angle BFE+\angle EFD=180°$.

Therefore, the angles$BFE$ and$EFD$ are the supplementary angles.

From the given diagram it can also be noticed that:

The angles$BFE$ and$EFD$ are not having same measure. Therefore, they are non- congruent angles.

Step 4. Write the name of the two non-congruent supplementary angles.

The angles$BFE$ and$EFD$ are non-congruent angles but they are supplementary angles.

Therefore, the name of the two non-congruent supplementary angles is$\angle BFE$ and $\angle EFD$.