In the context of the problem, if line AC is perpendicular to line BE, then ∡ABE and ∡DBE are adjacent angles.
To name the angle adjacent to ∡ABE specifically:
- ∡B refers to a single point, not an angle.
- ∡EBF is not directly adjacent to ∡ABE.
- ∡DBE is actually adjacent to ∡ABE.
- ∡FBC is also not directly adjacent to ∡ABE.
Thus, the correct answer is ∡DBE.