Question

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

Answer 1

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°

Answer 2

Answer:

angle OSR = 35°

angle OSP = 55°

Step-by-step explanation:

In rectangle PQRS, the diagonal PR and SQ intersect at O.

Given, angle ROS = 110°

Now, in rectangle diagonals are equal and bisect each other.

Then SO = RO

In ΔROS,

∠OSR = ∠ORS

Now, ∠ROS + ∠OSR + ∠ORS = 180°

         110° + 2∠OSR = 180°

          2∠OSR = 70°

          ∠OSR = 70°/2

          ∠OSR = 35°

and ∠OSR + ∠OSP = 90°

       35° + ∠OSP = 90°

       ∠OSP = 90° - 35°

       ∠OSP = 55°