In fig find the values of $$x$$ and $$y$$ and then show that $$AB \parallel CD$$


Here, $$\angle x+50^0=180^0$$--- straight line
$$\angle x=180^0-50^0$$
$$\angle x=130^0$$
And $$\angle y=130^0$$ --- vertically opposite angles
Thus, $$\angle x =\angle y=130^0$$
Using Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
Thus, $$AB\parallel CD$$