The hour hand on a clock is between 2 and 3. What is the angle between the hour hand and the 12?

To determine the angle between the hour hand and the 12 on a clock when the hour hand is between 2 and 3, one can use the understanding that each hour mark on the clock represents a division of the full circle of 360 degrees.

The formula for calculating the angle of the hour hand relative to the 12 o'clock position is based on the number of hours passed and the fraction of the hour that has gone by. Since each hour accounts for 30 degrees (360 degrees divided by 12 hours), we can apply this to the situation:

1. At 2:00, the hour hand is exactly at the 2, which is 60 degrees from the 12 (2 hours × 30 degrees).
2. As time progresses towards 3, the hour hand will move further. For every minute that passes, the hour hand moves by 0.5 degrees (30 degrees per hour divided by 60 minutes).

If we consider that the hour hand is, for instance, at 2:30, it would be positioned halfway between 2:00 and 3:00. Thus, it would be at 75 degrees (60 degrees at 2:00 + 15 degrees for the additional half