In Fig. 6.43, if PQ⊥PS, PQ∥SR, ∠SQR=28° and ∠QRT=65°, then find the values of x and y.

Given, PQ⊥PS, PQ∥SR, ∠SQR=28°, ∠QRT=65°
According to the question,
x+∠SQR=∠QRT (Alternate angles as QR is transversal)
⇒x+28°=65°
⇒x=37°
Also ∠QSR=x ⇒∠QSR=37°
Also ∠QRS+∠QRT=180° (Linear pair)
⇒∠QRS+65°=180°
⇒∠QRS=115°
Now, ∠P+∠Q+∠R+∠S=360° (Sum of the angles in a quadrilateral)
⇒90°+65°+115°+∠S=360°
⇒270°+y+∠QSR=360°
⇒270°+y+37°=360°
⇒307°+y=360°
⇒y=53°