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    Question

    In triangle △ ABC, the internal angle bisectors of ∠

    B and ∠ C intersect at point OO. If the measure of ∠ BAC = 50o , determine the measure of ∠ BOC. 
    A 65º Correct Answer Incorrect Answer
    B 105º Correct Answer Incorrect Answer
    C 75º Correct Answer Incorrect Answer
    D 115º Correct Answer Incorrect Answer

    Solution

    Let ∠ ABC = 2xo and ∠ ACB = 2yo Sum of all the angles of a triangle is 180o So, ∠ BAC + ∠ BCA + ∠ CBA = 180o Or, 50o + 2x + 2y = 180o Or, 2x + 2y = 130o Or, x + y = 65o Again, in ΔBOC, ∠ BOC + ∠ BCO + ∠ CBO = 180o So, ∠ BOC + x + y = 180o So, ∠ BOC = 180o – 65o = 115o 

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