Question:
What is the number of degrees in the measure of the smaller obtuse angle formed by the hands of a standard clock at 2:48pm?

Answer:
[asy]
unitsize(0.8inch);
for (int i=0 ; i<=11 ;++i)
{
draw((rotate(i*30)*(0.8,0)) -- (rotate(i*30)*(1,0)));
label(format("%d",i+1),(rotate(60 - i*30)*(0.68,0)));
}
draw(Circle((0,0),1),linewidth(1.1));
draw(rotate(162)*(0.7,0)--(0,0)--(rotate(6)*(0.5,0)),linewidth(1.2));
[/asy]

There are 12 hours on a clock, so each hour mark is $360^\circ/12 = 30^\circ$ from its neighbors.  At 2:48 the minute hand points at minute 48, which is $\frac35$ of the way from hour 9 to hour 10.  Therefore, the minute hand is $\frac35\cdot 30 = 18^\circ$ past hour 9, which means it is $30^\circ - 18^\circ = 12^\circ$ shy of hour 10.  This means the minute hand is $2\cdot 30^\circ + 12^\circ = 72^\circ$ shy of hour 12.

The hour hand is $\frac{48}{60} = \frac45$ of the way from hour 2 to hour 3, so it is $\frac45\cdot 30^\circ = 24^\circ$ past hour 2.  So, the hour hand is $2\cdot 30^\circ + 24^\circ = 84^\circ$ past hour 12.

Combining the angles between each hand and hour 12, the angle between the hands is $72^\circ + 84^\circ = \boxed{156^\circ}$.