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

#### Solution

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, $AB\parallel CD$