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Question

In fig 3.32 . If $$AB | | CD , \angle APQ = 50^{\circ} $$ and $$ \angle PRD = 127^{\circ}$$ , find x and y 
1869751_319231700026408a8431765d50932e35.PNG


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 
$$\therefore \angle APR = \angle PRD $$
$$\angle APQ + \angle QPR = \angle PRD $$
$$50 + \angle QRP = 127 $$
$$\angle QPR = 127 - 50$$
$$\therefore \angle QPR = 77^{\circ}$$
$$\angle QPR = y = 77^{\circ}$$
$$\therefore  x = 50^{\circ}$$
$$y = 77^{\circ}$$

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