In the figure,find the values of $x$ and $y$ and then show that $AB \parallel CD$.
(N/A) From the figure,the line $PQ$ intersects the line $CD$ at point $F$.
Therefore,$y = 130^o$ (Vertically opposite angles) .......... $(1)$
Now,consider the line $AB$. The angle $x$ and the angle $50^o$ form a linear pair at the intersection point $E$.
Therefore,$x + 50^o = 180^o$ (Linear pair axiom)
$x = 180^o - 50^o = 130^o$ .......... $(2)$
From $(1)$ and $(2)$,we have $x = y = 130^o$.
Since these are alternate interior angles and they are equal,the lines $AB$ and $CD$ must be parallel.
Therefore,$AB \parallel CD$.
Therefore,$y = 130^o$ (Vertically opposite angles) .......... $(1)$
Now,consider the line $AB$. The angle $x$ and the angle $50^o$ form a linear pair at the intersection point $E$.
Therefore,$x + 50^o = 180^o$ (Linear pair axiom)
$x = 180^o - 50^o = 130^o$ .......... $(2)$
From $(1)$ and $(2)$,we have $x = y = 130^o$.
Since these are alternate interior angles and they are equal,the lines $AB$ and $CD$ must be parallel.
Therefore,$AB \parallel CD$.
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