Answer
$m \angle 1 = 94^{\circ}$
$m \angle 2 = 132^{\circ}$
Work Step by Step
This quadrilateral is a trapezoid; it has exactly one pair of parallel sides.
If we take a look at the diagram, we see that we have two transversals. The angles formed by each transversal are, in actuality, alternate interior angles; these types of angles are supplementary. Let's set up the equation to find $m \angle 1$:
$m \angle 1 = 180 - 86$
Subtract to solve:
$m \angle 1 = 94^{\circ}$
Let's set up an equation to find $m \angle 2$:
$m \angle 2 = 180 - 48$
Subtract to solve:
$m \angle 2 = 132^{\circ}$
