Q. 54.3( 330 Votes )

# 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 = 50o and,

PRD = 127o

According to question,

x = 50o (Alternate interior angle)

PRD + ∠PRQ = 180o (Angles on the straight line are supplementary)

127o + ∠PRQ = 180o

∠PRQ = 53o

Now,

In Δ PQR,

x + y + ∠PRQ = 180o  (Sum of interior angles of a triangle)

y + 50o + ∠ PRQ = 180o

y + 50o + 53o = 180o

y + 103o = 180o

y = 77o

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