at 3.20 am, what will be the angle between the hour hand and the minute hand?

The angle between the hour hand and the minute hand at 3:20 a.m. is 20°.

Quick Scoop

To see why, imagine how each hand moves:

• A clock is a full circle of 360°, divided into 12 hours.
• Each hour mark is 360÷12=30360÷12=30360÷12=30 degrees apart.
• The minute hand moves 666 degrees per minute (because 360÷60=6360÷60=6360÷60=6).
• The hour hand moves 0.50.50.5 degrees per minute (because it moves 30° in 60 minutes).

Step-by-step:

1. Hour hand position at 3:20
   • At 3:00, the hour hand is at 3×30=90°3×30=90°3×30=90°.
   • In 20 minutes, it moves 20×0.5=10°20×0.5=10°20×0.5=10°.
   • So at 3:20, the hour hand is at 90+10=100°90+10=100°90+10=100°.

2. Minute hand position at 3:20
   • The minute hand at 20 minutes: 20×6=120°20×6=120°20×6=120° from 12 o’clock.

3. Angle between the hands
   • Difference =∣120−100∣=20°=|120-100|=20°=∣120−100∣=20°.

So, at 3:20 a.m. , the angle between the hour and minute hands is 20 degrees.