Question

In the given figure, the the values of x and y and then show that AB||CD​

Answer 1

130° is congruent to angle y (vertically opposite angles)

Therefore, Angle y = 130°

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50° + angle x = 180° (angles in linear pair)

Therefore, angle x = 180°- 50°

= 130°

Therefore, Angle x = 130°

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Angle x = 130° -> equation 1

Angle y = 130° -> equation 2

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From equations 1 and 2,

Angle x = Angle y

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Therefore, by alternate angles test (If the alternate angles formed on two lines are congruent, then the lines are parallel),

Line AB || Line CD

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Hope it helps.

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