Final answer:
The relationship between the angles ∡ABF and ∡FBE can be vertical, supplementary, or complementary, but additional context is needed to determine which one.
Step-by-step explanation:
The relationship between ∡ABF and ∡FBE depends on the context provided in a diagram or additional information. Without more information, we cannot definitively determine whether the angles are vertical, supplementary, or complementary. If ∡ABF and ∡FBE are vertical angles, they would be equal in measure. If they are supplementary, their measures would add up to 180 degrees. If they are complementary, their measures would add up to 90 degrees. It's important to assess the given angles in the context of the problem to determine their relationship correctly.