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Question

In fig 3.28. Find the values of x and y and then show that $$AB | | CD $$
Show that $$AB | | CD . $$
1869687_aae1b816acee402498087ef7a74e5a8d.PNG


Solution

PQ Bisects AB at R 
$$\angle PRA $$ and $$\angle ARS $$ are on straight line PQ 
$$\therefore \angle PRA + \angle ARS = 180^{\circ}$$ Adjacent angles 
$$50 + \angle ARS = 180^{\circ}$$\
$$\angle ARS = 180 - 50$$
$$\therefore x = \angle ARS = 130^{\circ} $$

PQ straight line intersects straight line CD at S 
$$\therefore \angle CSQ = \angle RSD $$ . Vertically opposite angles 
$$\therefore y = \angle RSD = 130^{\circ}$$

Therse are mutal alternative angles 
$$\therefore x = y = 130^{\circ}$$
$$\therefore AB | | CD $$
1830121_1869687_ans_bfece6f764a244559a5c485f37aa7dff.PNG

Maths

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