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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.
Solution
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]
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