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Question -

In figure, find the values of x and y and then show that AB || CD.



Answer -

In the figure, we have CD and PQ intersect at F.
┬а
тИ┤ y = 130┬░ тАж(1)
[Vertically opposite angles]
Again, PQ is a straight line and EA stands on it.
тИаAEP + тИаAEQ = 180┬░ [Linear pair]
or 50┬░ + x = 180┬░
тЗТ x = 180┬░ тАУ 50┬░ = 130┬░ тАж(2)
From (1) and (2), x = y
As they are pair of alternate interior angles.
тИ┤ AB || CD

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