Question

# In fig 3.32 . If $$AB | | CD , \angle APQ = 50^{\circ}$$ and $$\angle PRD = 127^{\circ}$$ , find x and y

Solution

## If $$AB | | CD$$ and $$\angle APQ = 50^{\circ}$$ and $$\angle PRD = 127^{\circ}$$ , then $$\angle x = ? \angle y = ?$$$$\therefore \angle APQ = \angle PQR = x$$$$50 = \angle PQR = x$$$$\therefore x = 50^{\circ}$$similarly , $$AB | | CD PR$$ straight line intersects these at P and R $$\therefore \angle APR = \angle PRD$$$$\angle APQ + \angle QPR = \angle PRD$$$$50 + \angle QRP = 127$$$$\angle QPR = 127 - 50$$$$\therefore \angle QPR = 77^{\circ}$$$$\angle QPR = y = 77^{\circ}$$$$\therefore x = 50^{\circ}$$$$y = 77^{\circ}$$Maths

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