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    Question

    ABCD is a cyclic quadrilateral, such that ratio of

    measures ∠A, ∠B and ∠C is 1 : 4 : 5, then the measure of ∠D is.
    A 40° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 60° Correct Answer Incorrect Answer
    D 120° Correct Answer Incorrect Answer

    Solution

    The sum of the opposite angles in cyclic quadrilateral is 180° ∠A = 1x ∠B = 4x ∠C = 5x ∠A + ∠C = 180° 1x + 5x = 180° x = 30° ∠B = 4 × 30° = 120° ∠B + ∠D = 180° 120° + ∠D = 180° ∠D = 60°

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