Question

In the given figures below, decide whether l is parallel to m.

Answer 1

As we know vertically opposite angles are equal. So at the point of intersection of line $l$ and $n$ vertically opposite angle of ${75}^{\circ }$ is also ${75}^{\circ }$.
Now, $n$ is transversal to line $l$ and $m$ and,
${75}^{\circ }+{75}^{\circ }={150}^{\circ }$
$\Rightarrow$Sum of interior angles on the same side of transversal is not ${180}^{\circ }$
$\Rightarrow$$l$ is not parallel to $m$ because sum of angles does not obey the property of parallel lines.