In this image, we are tasked with identifying the vertical angles given that $\overline{IK}$ and $\overline{LN}$ are parallel lines.

Vertical angles are pairs of non-adjacent angles formed when two lines intersect. They are always congruent to each other.

In the diagram, we see two transversals intersecting the parallel lines. Specifically:

• One transversal intersects at points $M$ and $J$, creating multiple angles.

Looking for vertical angles:

1. $\angle KJH$ and $\angle IJM$ are vertical angles, as they are opposite each other at the intersection point $J$.
2. $\angle IJH$ and $\angle KJM$ are vertical angles as well, as they are opposite each other at the same point $J$.

Among the provided answer choices:

• $\angle KJH$ and $\angle IJM$ are vertical angles.

Thus, the correct answer is $\angle KJH$ and $\angle IJM$.

Would you like further details or have any questions?

Here are some related questions you could explore:

1. What are corresponding angles and how are they formed in this diagram?
2. How do we know that vertical angles are always congruent?
3. What are alternate interior angles, and can they be identified here?
4. Can we find supplementary angles in this diagram?
5. How does the fact that $\overline{IK}$ and $\overline{LN}$ are parallel help in identifying angle relationships?

Tip: Vertical angles are always congruent, regardless of whether the lines are parallel or not.