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    Question

    What is the ∠ SRO if O is the centre of circle,

    ∠ SPO = 55˚ and ∠ POR = 115 ˚
    A 66.5˚ Correct Answer Incorrect Answer
    B 77.5˚ Correct Answer Incorrect Answer
    C 69.5˚ Correct Answer Incorrect Answer
    D 67.5˚ Correct Answer Incorrect Answer

    Solution

    In quadrilateral PQRS, ∠ SRQ = 180˚ - ∠ SPO = 180˚ - 55˚= 125˚ [Sum of opposite angle of a cyclic quadrilateral is 180˚.] ∠ ROQ = 180˚ - ∠ POR = 180˚ - 115˚ = 65˚ In △ QOR, ∠ OQR = ∠ ORQ [Angles opposite of same side] ∠ ROQ + ∠ OQR + ∠ ORQ = 180˚ 65˚ + ∠ ORQ + ∠ ORQ = 180˚ ∠ ORQ = (180˚ - 65˚)/2 = 57.5˚ ∠ SRO = ∠ SRQ - ∠ ORQ = 125˚ - 57.5 ˚ = 67.5 ˚

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