What is the angle made between the hour and the minute hand of the clock ?.

In reference to $12$ the hour hand moves $0.5^\circ$ per minute, so at $3:15$ the hour hand moved $0.5[3(60)+15]=97.5^\circ$ .

In reference to $12$ the minute moves $6^\circ$ per minute, so at $3:15$ the minute hand moved $15(6) = 90^\circ$ .

Therefore, the angle formed is $97.5-90=\boxed{7.5^\circ}$ .

At 3:15 the minute hand is at 3, the hour hand advances 30/4 = 7.5 degrees. For every hour the hour hand moves by 30 degrees and so for 15 minutes it moves by 7.5 degrees.