Question

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

Answer 1

If AB||CD and ∠APQ= 50° and 

∠PRD = 127°, then ∠x = ? 

∠y = ? 

AB||CD PQ straight line intersects these at P and Q. 

∴ ∠APQ = ∠PQR . alternate angles. 

50 = ∠PQR = x 

∴ x = 50° 

Similarly, AB||CD PR straight line intersects these at P and R. 

∴ ∠APR = ∠PRD 

∠APQ + ∠QPR = ∠PRD 

50 + ∠QPR = 127 

∠QPR = 127 – 50 

∴∠QPR = 77 ° 

∠QPR = y = 77 ° 

∴ x = 50 °, 

y = 77 °.