Q18 of 50 Page 6

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

To Find: Values of x and y


Given: PQ is perpendicular to PS, PQ parallel SR


∠SQR = 28o


And, ∠QRT = 65o


Now according to the question,


x + ∠SQR = ∠QRT (Alternate angles are equal as QR is transversal)


x + 28o = 65o


x = 37o


Now, in Δ PQS, Sum of interior angles of a triangle = 180°


∠ PQS + ∠ PSQ + ∠ QPS = 180°


Therefore,


y + 37° + 90° = 180°


y = 53°


So, x = 37° and y = 53°


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