Question

AB,CD&EF are three concurrent lines passing through the point O such that OF bisects angle BOD. If angle BOF = 35degrees. Find angle BOC & angle AOD​

Answer 1

Step-by-step explanation:

Lines AB,CD and EF intersect at O As OF bisects ∠BOD

⟹∠DOF=∠BOF=35(Given).....(1)

Also, AB is a straight line ⟹∠AOD+∠DOF+∠BOF=180(sum of angles formed by straight line is 180)

⟹∠AOD+35+35=180

⟹∠AOD=180−70=110

Now∠AOD=∠BOC

(Vertically opposite angle) ⟹∠BOC=110

solution

Answer 2

Answer:

∠BOC = 110° and ∠AOD = 110°

Step-by-step explanation:

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°

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