Question

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

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 $$\therefore x = y = 130^{\circ}$$$$\therefore AB | | CD$$Maths

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