jmc

There are 12 hours on a clock, so each hour mark is $360^{\circ }/12=30^{\circ }$ from its neighbors. At 2:30, the minute hand points at the 6, while the hour hand is mid-way between the 2 and the 3. Therefore, the hour hand is $\frac{1}{2}\cdot 30^{\circ }=15^{\circ }$ from the 3 on the clock, and there are $3\cdot 30^{\circ }=90^{\circ }$ between the 3 and the 6 on the clock. So, the hour and the minute hand are $15^{\circ }+90^{\circ }=\boxed{105^{\circ }}$ apart.