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    Question

    In a quadrilateral PQRS, the bisectors of ∠R and ∠S

    intersects each other at point 'O'. Find the ∠Q if ∠P = 75o and ∠ROS = 95o.
    A 115° Correct Answer Incorrect Answer
    B 95° Correct Answer Incorrect Answer
    C 105° Correct Answer Incorrect Answer
    D 125° Correct Answer Incorrect Answer

    Solution

    Image
    In ΔROS;

    We have, ∠ROS + ∠ORS + ∠OSR = 180o

    Or, 95o + ∠ORS + ∠OSR = 180o

    Or, ∠ORS + ∠OSR = 85o

    Or, (∠R/2) + (∠S/2) = 85o {∠ORS = (∠R/2) and ∠OSR = (∠S/2) }

    So, ∠R + ∠S = 170o

    We know that sum of each angle of a quadrilateral is 360o.

    So, ∠P + ∠Q + ∠R + ∠S = 360o

    Or, 75o + ∠Q + 170O = 360o

    Or, ∠Q = 360o - 245o

    So, ∠Q = 115o

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