Answer: ∠FEA is supplementary to ∠FEB and to ∠HGD if ∠FEA and ∠HGC are congruent and if AEB and CGD are straight lines.
Step-by-step explanation:
Sorry if that is too much info. The questions is a little oddly worded.
Supplementary angles are 2 angles that together equal 180° so if AEB and CGD are straight lines then they equal 180°. Assuming that the 2 diagrams are congruent (the same) on all matching angles then ∠FEA and ∠HGC are the same and ∠FEB and ∠HGD are the same.
Therefore
∠FEA + ∠FEB = 180°
∠FEA + ∠HGD = 180°
likewise
∠HGC + ∠FEB = 180°
∠HGC + ∠HGD = 180°
meaning those specific 4 parings are all supplementary .