The angle between the hour hand and the minute hand of a clock at 3:30 can be calculated using the clock angle formula:

• The hour hand moves 30° per hour plus 0.5° per minute.
• The minute hand moves 6° per minute.

At 3:30:

• Hour hand angle = 30×3+0.5×30=90+15=105∘30\times 3+0.5\times 30=90+15=105^\circ 30×3+0.5×30=90+15=105∘
• Minute hand angle = 6×30=180∘6\times 30=180^\circ 6×30=180∘

The angle between them is the absolute difference:

∣180∘−105∘∣=75∘|180^\circ -105^\circ|=75^\circ ∣180∘−105∘∣=75∘

Therefore, the angle between the hour hand and the minute hand at 3:30 is 75 degrees

. Note: Some sources incorrectly state the angle as 90 degrees by assuming the hour hand is fixed exactly at 3, but since the hour hand moves as the minutes pass, the correct angle is 75 degrees.