In triangle abc the angle bisectors of angle b and angle c meet at 0. If angle a is 70 degree find angle boc

Ankush Jain , Meritnation Expert added an answer, on 13/7/12

**Given,** ∠BAC = 70°.

Now, in △ ABC using angle sum property of triangle, we have

∠ABC + ∠ACB + ∠BAC = 180°

⇒∠ABC + ∠ACB + 70° = 180°

⇒ ∠ABC + ∠ACB = 180° - 70° = 110°

⇒ 2∠OBC + 2∠OCB = 110° [Given BO and CO are bisectors of ∠ABC and ∠ACB respectively. So, ∠ABC = 2∠OBC and ∠ACB = 2∠OCB]

⇒ ∠OBC + ∠OCB = 55°

In △ BOC using angle sum property of triangle, we have

∠OBC + ∠OCB + ∠BOC = 180°

⇒ 55° + ∠BOC = 180°

⇒ ∠BOC = 180° - 55° = 125°

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