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Question

In the figure, in ∆ABC, the angle bisectors of ∠B and ∠C meet at a point O. Find the measure of ∠BOC.
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Solution

In ABC, using angle sum property, we have: CAB + ABC + BCA = 180°70° + ABC + BCA = 180° ABC + BCA = 110° -----1 Now,BO is the angle bisector of ABC. OBC = 12ABCandCO is the angle bisector of BCA. OCB = 12BCAOBC + OCB = 12ABC + BCA-----2In OBC, using angle sum property, we get: BOC + OBC + OCB = 180°Using 2 we get: BOC + 12ABC + BCA = 180°Now, using 1 we get: BOC + 12110° = 180°BOC + 55° = 180°BOC = 180°-55°= 125°Therefore, BOC = 125°

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