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    Question

    In a ΔABC, the internal bisectors of ∠B and ∠C meet

    at point O. Find the measure of ∠BOC if the measure of ∠BAC = 50 ° .
    A 65° Correct Answer Incorrect Answer
    B 105° Correct Answer Incorrect Answer
    C 75° Correct Answer Incorrect Answer
    D 115° Correct Answer Incorrect Answer

    Solution

    Image


    Let ∠ABC = 2x o  and ∠ACB = 2y o

    Sum of all the angles of a triangle is 180 o

    So, ∠BAC + ∠BCA + ∠CBA = 180 o

    50 o  + 2x + 2y = 180 °

    2x + 2y = 130 °

    x + y = 65 °

    Again, in ΔBOC, ∠BOC + ∠BCO + ∠CBO = 180 o

    So, ∠BOC + x + y = 180 °

    So, ∠BOC = 180 °  – 65 °   = 115 °

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