Sum of internal angles of pentagonal BCEFO

∠B+∠C+∠E+∠F+∠BOF=540

∠AHG is the external angle of △HDG.

∠AHG=∠D+∠G

∠BOF is the external angle of △OAH.

∠BOF=∠AHG+∠A

∠BOF=∠A+∠D+∠G

∠A+∠b+∠C+∠E+∠F+∠G =∠b+∠C+∠E+∠F+∠BOF = 540