Question

The diagonals of a rectangle PQRS intersect at O. If ∠ ROQ = 600, Find: (i) ∠ OSP (ii) ∠ RSO and (iii) ∠ PQO

Answer 1

Answer:

In the given figure, PQRS is a rectangle and its diagonals PR and QS intersect at O. If ∠POQ=110

o

, find the measure of ∠PSQ.

To find ∠PQO and ∠PSQ.

PQRS is a rectangle, and O is the intersection point of diagonals PR and SQ.

PR=SQ [Diagonals of rectangle are equal]

PO=Qo [Diagonals of rectangle bisect each other]

∴∠PQO=∠OPQ→(1) [Angles opposite to equal sides]

In △POQ ,

∠PQO+∠POQ+∠OPQ=180

∘

2∠PQO+110

∘

=180

∘

∠PQO=

2

180

∘

−110

∘

=35

∘

Now, in △PQS

∠PQS+∠QPS+∠PSQ=180

∘

35

∘

+90

∘

+∠PSQ=180

∘

∠PSQ=180

∘

−125

∘

=55

∘

I hope it helps you