5. In Fig. 6.32, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.
Solution: From the diagram, ∠APQ = ∠PQR (Alternate interior angles) Now, putting the value of ∠APQ = 50° and ∠PQR = x we get, x = 50° Also, ∠APR = ∠PRD (Alternate interior angles) Or, ∠APR = 127° (As it is given that ∠PRD = 127°) We know that ∠APR = ∠APQ+∠QPR Now, putting values of ∠QPR = y and ∠APR = 127° we get, 127° = 50°+ y Or, y = 77° Thus, the values of x and y are calculated as: x = 50° and y = 77°
