Question

In the figure, if PT ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65°, then find the values of x and y.

Answer 1

In the given figure, lines PQ ⊥ PS, PQ || SR, 

∠SQR = 28° and ∠QRT = 65° 

∠PQR = ∠QRT [Alternate angles] 

⇒ x + 28° = 65° 

⇒ x = 65° – 28° = 37° 

In ∆PQS, 

∠SPQ + ∠PQS + ∠QSP = 180° [Angle sum property of a triangle] 

⇒ 90° + 37° + y = 180° 

[∵PQ ⊥ PS, ∠PQS = x = 37° and ∠QSP = y) 

⇒ 127° + y = 180° 

⇒ y = 180° – 127° = 53° 

Hence, x = 37° and y = 53° Ans.