The vertical angles among the given options are FGE and HGJ. Vertical angles are always congruent, ensuring that these angles share the same measure. Therefore, option D, FGE and HGJ, is the correct pairing.
Vertical angles are formed when two lines intersect. In this case, angles FGE and HGJ are vertical angles. Vertical angles are always congruent, meaning they have equal measures.
Therefore, FGE and HGJ have the same measure despite being on different sides of the intersection.
Options A, B, and C are incorrect because they pair FGE with angles IJL, FGJ, and HGE, respectively, which are not vertical angles.
Understanding the concept of vertical angles helps identify these geometric relationships and accurately select the correct pair, which, in this case, is option D (FGE and HGJ).