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    Question

    In a ∆ ABC, the bisectors of ∠ B and ∠ C meet

    at O. If ∠ BOC = 142°, then the measure of ∠ A is
    A 52° Correct Answer Incorrect Answer
    B 68° Correct Answer Incorrect Answer
    C 116° Correct Answer Incorrect Answer
    D 104° Correct Answer Incorrect Answer

    Solution

    Let, ∠B = x and ∠C = y OB and OC are two angle bisectors and meets at O. In ΔBCO, (x/2) + (y/2) + 142° = 180° ⇒ (x/2) + (y/2) = 38° ⇒ x + y = 76° In ΔABC, ∠B + ∠C = 76° ∠A = 180° – 76° ⇒ ∠A = 104° ∴ The measure of ∠A is 104°.

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