In the figure, if AB∥CD, ∠APQ=50 and ∠PRD=127, find x and y.

Given, AB∥CD, ∠APQ=50°, ∠PRD=127°
According to the question
x=50° (Alternate interior angles)
∠PRD+∠RPB=180° (Angles on the same side of transversal)
⇒127°+∠RPB=180°
⇒∠RPB=53°
Now, y+50°+∠RPB=180° (AB is a straight line)
⇒y+50°+53°=180°
⇒y+103°=180°
⇒y=77°
∴ x=50°, y=77°