Multiple choice

When the clock shows time 25 minutes past 2, the angle between the hands is.

  1. $75^o$
  2. $67 \dfrac{1}{2}^o$
  3. $77 \dfrac{1}{2}^o$
  4. $65^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 2:25, the minute hand is at 5 (25 minutes). The hour hand is at 2 + 25/60 = 2 + 5/12 = 29/12. The angle of the minute hand is 25 * 6 = 150 degrees. The angle of the hour hand is (29/12) * 30 = 72.5 degrees. The difference is 150 - 72.5 = 77.5 degrees.

AI explanation

Using the clock angle formula, the angle between the hands is the absolute value of 30 times the hour minus 5.5 times the minutes. At 2:25, this calculates to (30 * 2) - (5.5 * 25), which equals 60 - 137.5. The absolute difference between these values is 77.5 degrees, which is written as 77 1/2 degrees.

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