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 .

Question

AB, CD and EF are three concurrent lines passing through the point O such that OF bisects &#x2220; BOD . If &#x2220; BOF = 35&#xB0;, find &#x2220; BOC and &#x2220; AOD .

Philoid · Accepted Answer

OF bisects ∠BOD

∠BOF = 35^o

∠BOC =?

∠AOD =?

∠BOD = ∠BOF = 70^o(Therefore, OF bisects ∠BOD)

∠BOD = ∠AOC = 70^o(Vertically opposite angle)

∠BOC + ∠AOC = 180^o

∠BOC + 70^o = 180^o

∠BOC = 110^o

∠AOD = ∠BOC = 110^o(Vertically opposite angle)

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.