Question

AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.

Answer 1

OF bisects ∠BOD

∠BOF = 35°

∠BOC = ?

∠AOD = ?

∠BOD = ∠BOF = 70°(Therefore, OF bisects ∠BOD)

∠BOD = ∠AOC = 70°(Vertically opposite angle)

∠BOC + ∠AOC = 180°

∠BOC + 70° = 180°

∠BOC = 110°

∠AOD = ∠BOC = 110°(Vertically opposite angle)