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    Question

    Determine the measure of ∠SQT in the following figure

    given that ST = QT.
    A 114° Correct Answer Incorrect Answer
    B 66° Correct Answer Incorrect Answer
    C 48° Correct Answer Incorrect Answer
    D 76° Correct Answer Incorrect Answer

    Solution

    ATQ, Sum of opposite angles of a cyclic quadrilateral is 180° . So, ∠QSR  + ∠QPR  = 180° Or, 66°  + ∠QSR  = 180° Or, ∠QSR  = 180°  – 66° = 114° Sum of linear pairs of angle is 180° . So, ∠QSR  + ∠QST  = 180° Or, 114°  + ∠QS T = 180° Or, ∠QST  = 180°  – 114°  = 66° ST = QT So, ∠SQT  = ∠QST  (angles opposite to equal sides are equal) Therefore, ∠SQT  = 66°

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