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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.

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#### Solution

Given

OF bisects `∠`*B**O**D*

OF bisects `∠`*B**O**D*

*`∠`BOF *= 35°

*`∠`BOC *= ?

*`∠`AOD *= ?

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

`∠`*B**O**D *= `∠`*A**O**C *= 70° [ `∠`BODand `∠`AOCare vertically opposite angles]

Now,

* `∠`BOC *+ `∠`*AOC *= 180°

⇒ `∠`*BOC *+ 70° = 180°

⇒`∠`*BOC *= 110°

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

Concept: Pairs of Angles

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