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    Question

    In aΔPQR, the bisectors of ∠Q and ∠R meet at point

    O, inside the triangle. If ∠QOR = 107°, then the measure of ∠P is:
    A 40° Correct Answer Incorrect Answer
    B 23° Correct Answer Incorrect Answer
    C 17° Correct Answer Incorrect Answer
    D 34° Correct Answer Incorrect Answer

    Solution

    In ΔPQR, the angle bisectors of ∠Q and ∠R meet at O. Given: ∠QOR = 107° Using the angle bisector property: ∠QOR = 90° +∠P/2  Substitute the given value: 107° = 90° +∠P/2  ⟹ ∠P/2=17°  ⟹  ∠P = 34° 

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