Answer
$m\angle{1} = 108^o
\\m\angle{2} = 72^o
\\m\angle{3} = 108^o$
Work Step by Step
The 72-degree angle and angle $2$ are vertical angles, so they have the same measurements.
Thus,
$m\angle{2} = 72^o$
Angles 1 and 2 are supplementary, so their sum is 180 degrees.
Thus,
$m\angle{1} = (180^o-m\angle{2})
\\m\angle{1} = (180-72)^o
\\m\angle{1} = 108^o$
Angles 1 and 3 are vertical angles, so they have the same measurements.
Thus,
$m\angle{3} = m\angle{1} = 108^o$