# By calculating, I write the values of X and Y in the following rectangle PQRS:

Given PQRS is a rectangle

Each angle of a rectangle is 90°

Let O be the intersecting point of PR and QS

(i) SQR = 25°(given)

⇒∠PQS = 90° - 25° = 65°

And PSQ = 25° = SQR and QSR = PQS = 65°(PS QR and QS is transversal) and

Since the diagonals of rectangle are equal and bisects each other

In ΔQOR

OQ = OR

OQR = QRO = 25° (angles opposite to equal sides are equal)

QOR = 40° (angle sum property of a triangle)

SRQ = 90° (Each angle of a rectangle is 90°)

And QRP = 25° so PRS = x = 90° - 25° = 65°

In Δ PSO

PSQ = 25° and SPR = 25°

⇒∠POS = y = 90° - 50° = 40° (angle sum property of a triangle)

(ii) In rectangle PQRS

QOR = POS = 100° (vertically opposite angles)

In ΔPOS

PO = OS (diagonals of a rectangle are equal and bisects each other)

OPS = OSP = y

y = 180° - 100° =

x = 50°( each angle of rectangle is 90°)

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