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    Question

    MN is a diameter of a circle with centre O. The tangent

    at 'P' meets MN produced at 'Q'. If ∠PMN = 44 ° , then find ∠PNQ.
    A 134° Correct Answer Incorrect Answer
    B 124° Correct Answer Incorrect Answer
    C 104° Correct Answer Incorrect Answer
    D 144° Correct Answer Incorrect Answer

    Solution

    Image
    Angle made by the diameter of a circle on the arc of the circle is 90 o  i.e. ∠MPN = 90 ° .

    Sum of each angle in a triangle is 180 o .

    So, ∠PMN + ∠PNM + ∠MPN = 180 °

    Or, 44 °  + ∠PNM + 90 °  = 180 °

    Or, ∠PNM = 180 °  - 134 °

    Or, ∠PNM = 46 °

    Now, ∠PNM + ∠PNQ = 180 o  (Linear pair of angles)

    So, ∠PNQ = 180 - 46 = 134 °

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