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  ${\displaystyle \angle }$BOD

OF bisects  ${\displaystyle \angle }$BOD

${\displaystyle \angle }$BOF = 35°

${\displaystyle \angle }$BOC = ?

${\displaystyle \angle }$AOD = ?

∴${\displaystyle \angle }$BOD = 2 ${\displaystyle \angle }$BOF = 70°                    [ ∵ of bisects ${\displaystyle \angle }$BOD]

  ${\displaystyle \angle }$BOD = ${\displaystyle \angle }$AOC = 70°              [ ${\displaystyle \angle }$BODand ${\displaystyle \angle }$AOCare vertically opposite angles]

Now,

      ${\displaystyle \angle }$BOC + ${\displaystyle \angle }$AOC = 180°

⇒ ${\displaystyle \angle }$BOC + 70° = 180°

⇒${\displaystyle \angle }$BOC = 110°

∴ ${\displaystyle \angle }$AOD = ${\displaystyle \angle }$BOC = 110°               [Vertically opposite angles]