What is the angle between the hour and minute hands of a clock at 3:40?

The minute hand moves 360 degrees in 60 minutes, so 6 degrees a minute. The hour hand moves 30 degrees an hour, so half a degree a minute. The common slip is to put the hour hand exactly on 3 at 3:40; by then it has moved two thirds of the way towards 4. Formula: angle = |30H - 5.5M|.

Question: Angle between the hands at 3:40.

1. Minute hand from 12: 40 x 6 = 240 degrees.
2. Hour hand from 12: 3 x 30 + 40 x 0.5 = 90 + 20 = 110 degrees.
3. Difference = 240 - 110 = 130 degrees.

Formula check: |30 x 3 - 5.5 x 40| = |90 - 220| = 130.

If the formula gives more than 180, subtract from 360 to get the smaller angle. At 9:10, |270 - 55| = 215, so the smaller angle is 145 degrees.

const angle = (h, m) => {
  const a = Math.abs(30 * h - 5.5 * m);
  return Math.min(a, 360 - a);
};
console.log(angle(3, 40)); // Output: 130
console.log(angle(9, 10)); // Output: 145

• Keeping the hour hand fixed on 3 and answering 150 degrees.
• Forgetting to take 360 minus the result when it exceeds 180.