In the figure, transversal $l$, intersects two lines $m$ and $n, \angle 4 = 110^o$ and $\angle 7 = 65^o$. Is $m \parallel n$?
"
Given:
Transversal $l$, intersects two lines $m$ and $n, \angle 4 = 110^o$ and $\angle 7 = 65^o$.
To do:
We have to find whether $m \parallel n$.
Solution:
$\angle 4 = 110^o$ and $\angle 7 = 65^o$
$\angle 5 = \angle 7 = 65^o$ (Vertically opposite angles)
$\angle 4 + \angle 5 = 110^o + 65^o$
$ = 175^o$
Here, $\angle 4$ and $\angle 5$ are co-interior angles.
The sum of co-interior angles $\angle 4$ and $\angle 5$ is not $180^o$.
Therefore,
$m$ is not parallel to $n$.
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