Question

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

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

    Solution

    In quadrilateral PQRS, ∠ SRQ = 180Ëš - ∠ SPO = 180Ëš - 55Ëš= 125Ëš [Sum of opposite angle of a cyclic quadrilateral is 180Ëš.] ∠ ROQ = 180Ëš - ∠ POR = 180Ëš - 115Ëš = 65Ëš In â–³ QOR, ∠ OQR = ∠ ORQ [Angles opposite of same side] ∠ ROQ + ∠ OQR + ∠ ORQ = 180Ëš 65Ëš + ∠ ORQ + ∠ ORQ = 180Ëš ∠ ORQ = (180Ëš - 65Ëš)/2 = 57.5Ëš ∠ SRO = ∠ SRQ - ∠ ORQ = 125Ëš - 57.5 Ëš = 67.5 Ëš

    Practice Next

    Relevant for Exams: