Answer
$m \angle 1 = 135^{\circ}$
$m \angle 2 = 135^{\circ}$
$m \angle 3 = 45^{\circ}$
Work Step by Step
According to theorem 6-19, the base angles of an isosceles trapezoid are congruent; therefore, if one of the base angles is $45^{\circ}$, the other base angle, $\angle 3$, is $45^{\circ}$.
The other two angles of this trapezoid are supplementary to these base angles and are congruent to one another. Let's set the angles equal to $45^{\circ}$ subtracted from $180^{\circ}$:
$m \angle 1 = m \angle 2 = 180^{\circ} - 45^{\circ}$
Subtract to solve:
$m \angle 1 = m \angle 2 = 135^{\circ}$
