jmc

Let the angles be $a$, $a+d$, $a+2d$, and $a+3d$, from smallest to largest. Note that the sum of the measures of the smallest and largest angles is equal to the sum of the measures of the second smallest and second largest angles. This means that the sum of the measures of the smallest and largest angles is equal to half of the total degrees in the trapezoid, or $180^{\circ }$. Since the largest angle measures $120^{\circ }$, the smallest must measure $180^{\circ }-120^{\circ }=\boxed{60^{\circ }}$.