Question

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

Answer 1

$x+{50}^{\circ }={180}^{\circ }$ (Linear pair)

$\Rightarrow x={130}^{\circ }$

Also, $y={130}^{\circ }$ (Vertically opposite)

Now, $x=y={130}^{\circ }$ (Alternate interior angles)

Alternate interior angles are equal.

$\therefore AB\parallel CD.$