Question

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

Answer 1

It is given that PQ || SR and QR is a transversal line.

∠PQR = ∠QRT (Alternate interior angles)

x + 28 = 65

x = 65 − 28

x = 37

By using the angle sum property for ΔSPQ, we obtain

∠SPQ + x + y = 180

90 + 37 + y = 180

y = 180 − 127

y = 53

∠x = 37 and y = 53