If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

In the following figure, $\angle 1=60°$ and $\angle 2={\left(\frac{2}{3}\right)}^{rd}$ of a right angle. Prove that $l \Vert m$.

In the following figure, if $l \Vert m \Vert n$ and $\angle 1=60°,$ find $\angle 2$

In the following figure, $p$ is a transversal to lines $m$ and $n, \angle 2=120°$ and $\angle 5=60°.$ Prove that $m \Vert n$.