Question

The diagonals of rectangle PQRS meet at point O. If PR = 18 cm, find the
length of OQ.

Answer 1

Answer:

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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 , angle PQO 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, angle PQO = angle OPQ ……………1

Now in triangle POQ ,

Angle PQO + angle POQ + angle OPQ = 180°

angle PQO + 110 + angle PQO c = 180 (from eqn 1)

2 angle PQO = 180-110

angle PQO = 70/2 = 35°

now , in triangle PQS

angle PQS + angle QPS +angle PSQ = 180

35 + 90 + angle PSQ = 180

125 + angle PSQ = 180

angle PSQ = 180-125 = 55°