Multiple choice

Find the angle between the two hands of a clock of $15$ minutes past $4$ O' clock.

  1. $38.5^{\circ}$
  2. $36.5^{\circ}$
  3. $37.5^{\circ}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 4:15, the hour hand is at 4 + 15/60 = 4.25 hours. The position in degrees from 12 is 4.25 * 30 = 127.5 degrees. The minute hand is at 15 minutes, which is 15 * 6 = 90 degrees. The difference is 127.5 - 90 = 37.5 degrees.

AI explanation

Using the clock angle formula, we calculate the angle as 30 times the hours minus 5.5 times the minutes. Substituting the values for 4:15, we get 120 minus 82.5, which equals 37.5 degrees. The angle between the two hands is 37.5 degrees.

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