The problem asks which angles are vertical angles. Vertical angles are pairs of angles that are opposite each other when two lines intersect, and they are always congruent (equal in measure).

In the diagram:

• $\overline{FH} \parallel \overline{IK}$, and $\overline{FJ}$ is the transversal.

From the choices:

1. $\angle FGJ$ and $\angle HGE$ - These angles are vertical angles because they are opposite each other where lines $\overline{FJ}$ and $\overline{GE}$ intersect.

So, the correct answer is:

• $\angle FGJ$ and $\angle HGE$.

Would you like further explanation or details? Here are some related questions to explore:

1. What are corresponding angles, and how do they relate to parallel lines?
2. How do alternate interior angles behave when parallel lines are cut by a transversal?
3. Can you explain the relationship between consecutive interior angles?
4. How do you calculate the measure of vertical angles if one angle is given?
5. How do you identify alternate exterior angles in a transversal?

Tip: Remember that vertical angles are always congruent because they share the same vertex but are on opposite sides of intersecting lines!