We consider a hand at the 12 to be $ 0^\circ $. Now we convert the hour and minute hands to a degree measure from $ 0^\circ $ to $ 360^\circ $. If we divide $ 360^\circ $ evenly among 60 minutes, we get that each minute, the minute hand moves $ \frac{360^\circ}{60}=6^\circ $. So if the minute hand is at 48 minutes, it is at $ 48\cdot6^\circ=288^\circ $. The hour hand is a little trickier. If we divide $ 360^\circ $ evenly among 12 hours, we get that each hour, the hour hand moves $ \frac{360^\circ}{12}=30^\circ $. Note that the hour hand is not at the 2 since it gradually moves toward the 3 throughout the hour. From the 2 toward the 3, the hour hand has moved $ \frac{48}{60}=\frac{4}{5} $ of the way. So the degree measure of the hour hand is $ 2\frac{4}{5}\cdot30^\circ=84^\circ $. To find the smaller angle formed by the two hands, we can find the larger angle $ 288^\circ-84^\circ=204^\circ $ and subtract from $ 360^\circ $ to get $ \boxed{156^\circ} $. Or we know that $ 84^\circ $ is coterminal with (ends at the same place as) $ 84^\circ+360^\circ=444^\circ $. Now we can subtract $ 444^\circ-288^\circ=\boxed{156^\circ} $ to find the smaller angle.