In Fig. 6.32, if AB || CD, ∠ APQ = 50° and∠ PRD = 127°, find x and y.

It is given in the question that:

AB parallel CD,

∠APQ = 50^o and,

∠PRD = 127^o

According to question,

x = 50^o (Alternate interior angle)

∠PRD + ∠RPB = 180^o (Angles on the same side of transversal)

127^o + ∠R{B = 180^o

∠RPB = 53^o

Now,

y + 50^o + ∠RPB = 180^o (Ab is a straight line)

y + 50^o + 53^o = 180^o

y + 103^o = 180^o

y = 77^o