To determine the angle between the hands of a clock at 9:30, follow these steps:
1. Understand the positions of the hour and minute hands on the clock:
- At 9:00, the hour hand is exactly at the 9 position.
- At 30 minutes past the hour, the minute hand is on the 6.
2. Calculate the degrees per hour and per minute:
- A clock is a circle with 360 degrees.
- There are 12 hours on a clock, so each hour mark represents 360° / 12 = 30°.
- There are 60 minutes in an hour, so each minute mark represents 360° / 60 = 6°.
3. Determine the angle of the hour hand at 9:30:
- The hour hand moves 30° per hour.
- Since the hour hand would be on the 9 at 9:00, we start there.
- By 9:30, the hour hand has moved halfway to the 10. So it moves another 30° / 2 = 15°.
- Therefore, at 9:30, the hour hand is at 9 30° + 15° = 285°.
4. Determine the angle of the minute hand at 9:30:
- The minute hand moves 6° per minute.
- At 30 minutes, the minute hand is at 30 6° = 180°.
5. Calculate the angle between the hour and minute hand:
- Subtract the minute hand's angle from the hour hand's angle: 285° - 180° = 105°.
- This is already the smaller angle since it is not greater than 180°.
Hence, the angle between the hands of the clock at 9:30 is 105 degrees.
Therefore, the correct answer is 105.
