Final answer:
The angle adjacent to ∠ILJ is ∠HLJ because it shares both a common side LJ and a common vertex L with ∠ILJ, without overlapping.
Step-by-step explanation:
To identify an angle adjacent to the given ∠ILJ, we need to look for another angle that has a common side and a common vertex with ∠ILJ but does not overlap with it. Among the options given:
- ∠FLH is not adjacent because it does not share a common side or vertex with ∠ILJ.
- ∠FLK is not adjacent because it does not share a common side or vertex with ∠ILJ.
- ∠HLJ has a common side LJ and a common vertex at L, making it adjacent to ∠ILJ.
- ∠KLJ is not adjacent because it shares a vertex and a side but overlaps with ∠ILJ.
Hence, the correct answer is C. ∠HLJ as it is the only angle that is adjacent to ∠ILJ.