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in Mathematics by (29.8k points)

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

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In the given figure, a transversal intersects two lines AB and CD such that 

x + 50° = 180° (Linear pair axiom) 

⇒ x = 180° – 50° 

= 130° y = 130° (Vertically opposite angles) 

Therefore, ∠x = ∠y = 130° (Alternate angles) 

∴ AB || CD (Converse of alternate angles axiom) Proved.

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