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    In a triangle PQR, incentre is A and ∠QAR = 116°. Find the measure of ∠QPR.
    Question

    In a triangle PQR, incentre is A and ∠QAR = 116°. Find the measure of ∠QPR.

    A.

    54o^o​​

    B.

    27o^o

    C.

    26o^o

    D.

    52o^o

    Correct option is D

    Given:

    In triangle PQR, the incenter is

    QAR=116,\angle QAR = 116^\circ,​​

    Concept Used:

    If PQR is a triangle and A is the incenter, then:

    QAR=90+P2\angle QAR = 90^\circ + \frac{\angle P}{2}​​

    Solution:

    QAR=90+P2\angle QAR = 90^\circ + \frac{\angle P}{2}

    Given that QAR=116,\angle QAR = 116^\circ,​ we substitute into the equation:

    116=90+P2116^\circ = 90^\circ + \frac{\angle P}{2}

    26=P226^\circ = \frac{\angle P}{2}​​

    P=52∠P = 52^\circ​​

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