In the given figure if PQ ⊥ PS; PQ // SR, ∠SQR = 28° and ∠QRT =

1.	In the given figure if PQ ⊥ PS; PQ // SR, ∠SQR = 28° and ∠QRT = 65°, then find the values of x and y.
Answer» Given that PQ ⊥ PS ; PQ // SR ∠SQR = 28°, ∠QRT = 65° From the figure ∠QSR = x° (∵ alt. int. angles for the lines PQ // SR) Also 65° = x + 28° (∵ ext. angles = sum of the opp. interior angles) ∴ x° = 65° – 28° = 37° And x° + y° = 90° [ ∵ PQ ⊥ PS and PQ // SR. ⇒ ∠P = ∠S] 37° + y = 90° ∴ y = 90° – 37° = 53°

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

Answer»

Given that PQ ⊥ PS ; PQ // SR

∠SQR = 28°, ∠QRT = 65°

From the figure

∠QSR = x° (∵ alt. int. angles for the lines PQ // SR)

Also 65° = x + 28°

(∵ ext. angles = sum of the opp. interior angles)

∴ x° = 65° – 28° = 37°

And x° + y° = 90°

[ ∵ PQ ⊥ PS and PQ // SR. ⇒ ∠P = ∠S]

37° + y = 90°

∴ y = 90° – 37° = 53°