To find the angle between the hour hand and the minute hand at 3:20 am, we use the clock angle formula:

1. Calculate the angle of the minute hand from 12 o'clock:

• The minute hand moves 6° per minute.
• At 20 minutes, angle = 6∘×20=120∘6^\circ \times 20=120^\circ 6∘×20=120∘.

2. Calculate the angle of the hour hand from 12 o'clock:

• The hour hand moves 30° per hour plus 0.5° per minute.
• At 3 hours and 20 minutes, angle = 30∘×3+0.5∘×20=90∘+10∘=100∘30^\circ \times 3+0.5^\circ \times 20=90^\circ +10^\circ =100^\circ 30∘×3+0.5∘×20=90∘+10∘=100∘.

3. Find the difference between the two angles:

• Difference = ∣120∘−100∘∣=20∘|120^\circ -100^\circ|=20^\circ ∣120∘−100∘∣=20∘.

Thus, the angle between the hour hand and the minute hand at 3:20 am is 20 degrees