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

Given

OF bisects  `∠`BOD

OF bisects  `∠`BOD

`∠`BOF = 35°

`∠`BOC = ?

`∠`AOD = ?

∴`∠`BOD = 2 `∠`BOF = 70°                    [ ∵ of bisects `∠`BOD]

  `∠`BOD = `∠`AOC = 70°              [ `∠`BODand `∠`AOCare vertically opposite angles]

Now,

      `∠`BOC + `∠`AOC = 180°

⇒ `∠`BOC + 70° = 180°

⇒`∠`BOC = 110°

∴ `∠`AOD = `∠`BOC = 110°               [Vertically opposite angles]