In the given figure, the value of x is 130° and the value of y is 130°.
From the given figure, it is noted that AB and CD are straight lines. Also, the transversal line passing through them is a straight line.
Since the angle subtended by a straight line is 180°, we can write that
∠x + 50°=180°
∠x =180°-50°
∠x =130°
Also, in the given figure, ∠y and 130° are vertically opposite angles because they are opposite to each other when two lines cross.
According to Vertical Angles Theorem, vertically opposite angles are equal (congruent). Therefore, the value of y is 130°.
So lines AB and CD cut by a transversal have a pair of alternate interior angles that are equal. Thus, by Antithesis of the Alternate Interior Angles Theorem, AB∥CD.