In Fig. 6.28, find the values of $ x $ and $ y $ and then show that $ \mathrm{AB}=\mathrm{CD} $.
"
To do:
We have to find the values of $x$ and $Y$ and then show that $AB \parallel CD$.
Solution:
We know that,
The sum of the measures of the angles in linear pairs is always $180^o$.
Since $x$ and $50^o$ are linear pairs of $AB$.
We get,
$x+50^o=180^o$
This implies,
$x=180^o-50^o$
Therefore,
$x=130^o$
We also know that,
Vertically opposite angles are equal.
Therefore, we get $y=130^o$ (since $X$ and $Y$ are vertically opposite angles)
Therefore,
$x=y=130^0$
We know that,
If alternate interior angles are equal, then the two lines are parallel.
Since,
$x$ and $y$ are alternate interior angles and are equal to one another
We get,
$AB \parallel CD$
Therefore,
$AB \parallel CD$
Hence proved.
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