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°)