Answer
$m \angle 1 = 38^{\circ}$
$m \angle 2 = 43^{\circ}$
$m \angle 3 = 99^{\circ}$
Work Step by Step
Let's find $m \angle 1$, which, along with the angle measuring $38^{\circ}$, is an alternate interior angle; therefore, $m \angle 1 = 38^{\circ}$.
Now that we have two of the three angle measures of a triangle, we can find the measure of the third angle using the triangle sum theorem, which states that the sum of the measures of the interior angles of a triangle equal $180^{\circ}$:
$m \angle 2 = 180 - (99 + 38)$
Evaluate what's in parentheses first, according to order of operations:
$m \angle 2 = 180 - (137)$
Subtract to solve:
$m \angle 2 = 43^{\circ}$
Opposite angles in a parallelogram are congruent; therefore, $m \angle 3 = 99^{\circ}$.
