Question

In the given figure, PQRS is a rectangle, if PRQ=30° , find the value of PQS

Answer 1

QS & PR intersect each other at O which is the mid point. because we know Diagonals of rectangle bisects each other.
Also we know Diagonals of the rectangle is equal. so dividing them by 2 we will get OQ= OR
hence OQR = ORQ = 30°
We know PQR = 90°
PQS + SQR = PQR
so PQS = PQR - SQR = 90° - 30° = 60°

Answer 2

Given:

Angle PRQ=30°

To find:

The angle PQS

Solution:
The angle PQS is 60°.

The angles P, Q, R, and S are right angles in the rectangle.

The diagonals of PQRS are of equal length and bisect one another.

PR=QS and PO=OR, OQ=OS.

In ΔQOR, OQ=OR

So, angle ORQ=angle OQR (Angles corresponding to equal sides)

angle ORQ=angle OQR=30°

In rectangle PQRS, Angle Q=90°

Angle Q=angle PQS+angle OQR

90°=angle PQS+30°

Angle PQS=60°

Therefore, the angle PQS is 60°.