In the figure,$\angle 1 = 60^{\circ}$ and $\angle 6 = 120^{\circ}$. Show that the lines $m$ and $n$ are parallel.

(N/A) We are given that $\angle 1 = 60^{\circ}$ and $\angle 6 = 120^{\circ}$.
From the figure,$\angle 5$ and $\angle 6$ form a linear pair.
Therefore,$\angle 5 + \angle 6 = 180^{\circ}$.
Substituting the value of $\angle 6$,we get $\angle 5 + 120^{\circ} = 180^{\circ}$.
$\angle 5 = 180^{\circ} - 120^{\circ} = 60^{\circ}$.
Now,we observe that $\angle 1 = 60^{\circ}$ and $\angle 5 = 60^{\circ}$.
Thus,$\angle 1 = \angle 5$.
Since $\angle 1$ and $\angle 5$ are corresponding angles and they are equal,the lines $m$ and $n$ must be parallel.