Given the diagram, we have the following information:

• $\overline{BD}$ and $\overline{EG}$ are parallel lines.
• $m \angle EFH = 125^\circ$.

We want to find $m \angle EFC$.

Solution

Since $\overline{BD} \parallel \overline{EG}$ and $\overline{AF}$ is a transversal, the corresponding angles are equal. $\angle EFH$ and $\angle EFC$ are corresponding angles.

Therefore, $m \angle EFC = m \angle EFH = 125^\circ$.

So, the measure of $\angle EFC$ is:

$m \angle EFC = 125^\circ$

Do you have any questions, or would you like further details?

Related Questions:

1. What are corresponding angles, and why are they equal in parallel lines?
2. How do we identify transversal lines in a diagram?
3. Can you find other corresponding angles in the given diagram?
4. What would be the measure of $\angle EFG$ if $\angle EFH = 125^\circ$?
5. If $\overline{EF}$ and $\overline{GH}$ were also parallel, what other relationships could be found?

Tip: When dealing with parallel lines and a transversal, identifying angle pairs like corresponding, alternate interior, and alternate exterior angles is crucial for solving such problems.