Question

This is my homework by the way.Given: m

Answer 1

Looking at the figure, we can determine the following relations:

A.

The angles ∠BFC and ∠DFE are vertical angles.

B.

The angles ∠BFA and ∠DFE are neither vertical angles or a linear pair.

C.

The angles ∠BFC and ∠CFD are a linear pair.

D.

The angles ∠AFE and ∠AFC are a linear pair.

E.

The angles ∠BFE and ∠CFD are vertical angles.

F.

The angles ∠AFE and ∠BFC are neither vertical angles or a linear pair.

Since the angle ∠EFD is 50° and the angles ∠AFB and ∠EFD are congruent, the angle ∠AFE can be found with the relation:

`\begin{gathered} \angle\text{AFE}+\angle\text{EFD}+\angle\text{AFB}=180 \\ \angle\text{AFE}+50+50=180 \\ \angle\text{AFE}=180-100 \\ \angle\text{AFE}=80\degree \end{gathered}`

The angles ∠DFC and ∠BFE are vertical angles, so we have:

`\begin{gathered} \angle\text{DFC}=\angle\text{BFE} \\ \angle\text{DFC}=\angle\text{BFA}+\angle\text{AFE} \\ \angle\text{DFC}=50+80 \\ \angle\text{DFC}=130\degree \end{gathered}`

The angles ∠BFC and ∠EFD are vertical angles, so they are congruent, therefore we have ∠BFC = 50°.