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

∠BOC = 110° and ∠AOD = 110°

Given,

AB, CD and EF are three concurrent lines passing through the point O

OF bisects ∠BOD

∠ BOF = 35°

Consider the attached figure, while going through the following steps

as OF bisects ∠BOD (given)

∠ BOF = ∠ FOD = 35°

from figure it's clear that,

∠ BOF + ∠ FOD + ∠ AOD = 180°

35° + 35° + ∠ AOD = 180°

70° + ∠ AOD = 180°

∠ AOD = 180° - 70° = 110°

∴ ∠ AOD = 110°

Now, consider ∠ BOC

∠ BOC = ∠ AOD  (vertically opposite angles are equal)

⇒ ∠ BOC = ∠ AOD = 110°

∴ ∠ BOC = 110°