Question

In the following figure PQRS is a square . Diagonal PR and QS meet at point O . If PO=2.5 cm QS=4x-3
Find
1) The Value of x
2)m∠POQ​

Answer 1

Answer:

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∘ [From (1)]

∠PQO=2180∘−110∘=35∘

Now, in △PQS

∠PQS+∠QPS+∠PSQ=180∘

35∘+90∘+∠PSQ=180∘

∠PSQ=180∘−125∘=55∘