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

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

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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.