In any triangle ABC, the base angles at B and C are bisected by BO and CO respectively. Then ∠BOC is ?->(Show Answer!)

1. In any triangle ABC, the base angles at B and C are bisected by BO and CO respectively. Then ∠BOC is

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By: anil on 05 May 2019 01.51 am

In $$ riangle$$ABC => $$angle$$A + $$angle$$B + $$angle$$C = $$pi$$ => $$frac{1}{2} (angle A + angle B + angle C) = frac{pi}{2}$$ => $$frac{angle B}{2} + frac{angle C}{2} = frac{pi}{2} - frac{angle A}{2}$$ In $$ riangle$$OBC => $$angle$$OBC + $$angle$$OCB + $$angle$$BOC = $$pi$$ => $$frac{angle B}{2} + frac{angle C}{2} + angle BOC = pi$$ => $$angle BOC = pi - (frac{pi}{2} - frac{angle A}{2})$$ = $$frac{pi}{2} + frac{angle A}{2}$$

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