– In a rectangle PQRS, the diagonals PR and SQ intersect at O and angle ROS = 110°. Find angle OSR and angle OSP.​

Question

– In a rectangle PQRS, the diagonals PR and SQ intersect at O and angle ROS = 110°. Find
angle OSR and angle OSP.​

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Ayla 13 hours 2021-10-13T09:45:05+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-13T09:46:41+00:00

    Step-by-step explanation:

    PQRS is a rectangle in which O is the intersection point of both the diagonals PR and QS

    We have angle POQ= 110°

    Now we need to find out , anglePQO and angle PSQ

    As we know in rectangle both the diagonals are equal

    So, PR = QS

    Also diagonals bisect each other

    So PO = QO

    Hence, anglePQO = angleOPQ ……………1

    Now in triangle POQ ,

    AnglePQO + anglePOQ + angleOPQ = 180°

    anglePQO + 110 + anglePQOc = 180 (from eqn 1)

    2 anglePQO = 180-110

    anglePQO = 70/2 = 35°

    now , in triangle PQS

    anglePQS + angleQPS +anglePSQ = 180

    35 + 90 + anglePSQ = 180

    125 + anglePSQ = 180

    anglePSQ = 180-125 = 55°

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