A wall clock shows the time as 12hr.15mts. Then what will be the angle between the two hands of the clock?

To calculate the angle between the hour angle and the minute angle when the time is 12hrs 15 minutes.

This is a time and motion problem.

Let us take 12 o'clock as reference point, when both hour and minute handle make zero angle. The angular speed of the minute handle is 360 degree/60 minute =6 degree per minute and that of the hour handle is 360 degree/12 hour = 360deg/(12*60) minute = 0.5 dgree minute.

So every minute, the minute handle has  the relative angular speed  of (6-0.5) degree with reference to the hour handle.

Therefore, the relative angular motion of the minute handle with respect to the hour handle after 15 minutes past 12 o'clock is (6-0.5)*15 =  82.5 degrees. In other words, the angle between the hour handle and minute handle at 12 hour 15 minutes is 82.5 degrees or 82 degree 30 minutes.