Multiple choice

Which of the following gives the acute angle formed between the hands (hour hand and minute hand) of a 12 hour clock at 7:40 AM?

  1. 15°

  2. 20°

  3. 10°

  4. 12°
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C Correct answer
Explanation

The position of the hour hand at 7:40 is 7 + 40/60 = 7 + 2/3 = 23/3 hours. Each hour is 30 degrees, so the hour hand is at (23/3) * 30 = 230 degrees from 12. The minute hand at 40 minutes is at 40 * 6 = 240 degrees. The angle is |240 - 230| = 10 degrees.

AI explanation

Using the clock angle formula, |30H - 5.5M|, where H is the hour and M is the minutes, we substitute H = 7 and M = 40. This gives |30(7) - 5.5(40)|, which equals |210 - 220|. The absolute difference is 10, so the acute angle formed is 10 degrees.

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