Let's analyze the diagram and problem.

We are given:

• $\overleftrightarrow{GI} \parallel \overleftrightarrow{JL}$
• $m \angle GHF = 61^\circ$
• We need to find $m \angle JKM$.

Key points:

• The lines $\overleftrightarrow{GI}$ and $\overleftrightarrow{JL}$ are parallel.
• $\overleftrightarrow{FKM}$ is the transversal intersecting these parallel lines.
• $\angle GHF$ and $\angle JKM$ are corresponding angles (angles on the same side of the transversal and on parallel lines), which means they are congruent.

Since corresponding angles are equal, we can conclude: $m \angle JKM = m \angle GHF = 61^\circ$

Thus, $m \angle JKM = 61^\circ$.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How do you identify corresponding angles in a transversal diagram?
3. What is the sum of angles around a point, and how does it help in solving problems with transversals?
4. Can parallel lines have supplementary angles? If so, in what situation?
5. How does knowing the angle relationships in parallel lines help solve real-world problems?

Tip: When dealing with transversals, always remember the corresponding, alternate interior, and alternate exterior angles formed by the parallel lines. These relationships are key to solving most problems!