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