Question

PQRS is a rectangle. Its diagonals PR and QS intersect each other at O. PR is produced to X such that Z SRX is 140°. Find the measure of the angles of A POQ. Hint: ZSRX + ZPRS = 180° and ZPRS= ZPSQ]​

Answer 1

Answer:

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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Answer 2

Answer:

55°

Step-by-step explanation:

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