Question

1. PQRS is a rectangle. find angle OPS,if angle QOR is 42degree
2.PQRS is a rectangle. find angle OPS,if angle QOR is 56 degree​

Answer 1

Answer:

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

Now in triangle POQ,

AnglePQO + anglePOQ + angleOPQ =

180°

Angle PQO + 11O + anglePQOc = 180 (from

eqn 1)

56

2anglePQO = 180 - 110

anglePQO = 70/2 = 35°

now, in triangle PQS

anglePQS + angleQPS + delta*Q = 180

35 +90 + IePSQ = 180

125 + anglePSQ = 18C

anglePSQ = 180-125 = 55°

Step-by-step explanation:

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Answer 2

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

Now in triangle POQ,

AnglePQO + anglePOQ + angleOPQ =

180°

Angle PQO + 11O + anglePQOc = 180 (from

eqn 1)

56

2anglePQO = 180 - 110

anglePQO = 70/2 = 35°

now, in triangle PQS

anglePQS + angleQPS + delta*Q = 180

35 +90 + IePSQ = 180

125 + anglePSQ = 18C

anglePSQ = 180-125 = 55°