Answer
False
Work Step by Step
The angle of $72^\circ$ and the supplementary angle of $m\angle1$ are corresponding angles, which means they are equal.
Therefore:
$72^\circ+m\angle1=180^\circ$
$m\angle1=108^\circ$
$m\angle1=m\angle2$, because they are vertical angles.
$m\angle2=108^\circ$
The statement is false.