The angle between the hour hand and the minute hand at 3:30 is 75°.

Quick Scoop

At 3:30, the hands are not at a right angle (so it’s not 90°); the hour hand has already moved ahead of 3, which reduces the gap between the two hands.

Step-by-step explanation

  1. Minute hand position
    • The minute hand moves 6° per minute (because 360° ÷ 60 minutes = 6° per minute).
 * At 30 minutes, angle from 12 o’clock:

Minute angle=30×6=180∘\text{Minute angle}=30\times 6=180^\circ Minute angle=30×6=180∘.

  1. Hour hand position
    • The hour hand moves 30° per hour (360° ÷ 12 hours = 30° per hour).
 * At 3:00, it is at 3×30=90∘3\times 30=90^\circ 3×30=90∘.

 * In 30 extra minutes, it moves further: the hour hand moves 0.5° per minute (30° ÷ 60).

 * Extra movement in 30 minutes: 30×0.5=15∘30\times 0.5=15^\circ 30×0.5=15∘.

 * So, hour hand angle at 3:30: 90∘+15∘=105∘90^\circ +15^\circ =105^\circ 90∘+15∘=105∘.
  1. Angle between the hands
    • Difference between their positions:
      ∣180∘−105∘∣=75∘|180^\circ -105^\circ|=75^\circ ∣180∘−105∘∣=75∘.

So, the angle between the hour and minute hands of a clock at 3:30 is 75 degrees.

Information gathered from public forums or data available on the internet and portrayed here.