Multiple choice

What is the angle between the hands of the clock when the time is 10 minutes past 5?

  1. $\displaystyle 95^{\circ}$
  2. $\displaystyle 105^{\circ}$
  3. $\displaystyle 92^{\circ}$
  4. $\displaystyle 98^{\circ}$
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A Correct answer
Explanation

At 5:10, the hour hand is at 5 + 10/60 = 5.166 hours. Each hour is 30 degrees, so the hour hand is at 5.166 * 30 = 155 degrees from 12. The minute hand is at 10 minutes * 6 degrees/min = 60 degrees from 12. Angle = 155 - 60 = 95 degrees.

AI explanation

Using the clock angle formula, we calculate the difference between 30 times 5 hours and 5.5 times 10 minutes. This yields 150 minus 55, which results in an angle of 95 degrees.

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