Multiple choice

What is the angle between the hour hand and minute hand of a clock at 5:35 PM?

  1. 42 ½0

  2. 46 ½0

  3. 48 ½0

  4. 50 ½0
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A Correct answer
Explanation

At 5:35 PM, the minute hand is at 7 (which corresponds to 210 degrees from 12 o'clock). The hour hand has moved past 5 by 35/60 of the space between 5 and 6, so its position is 5 * 30 + (35/60) * 30 = 150 + 17.5 = 167.5 degrees. The absolute difference between their positions is 210 - 167.5 = 42.5 degrees, which is written as 42 1/2 degrees (garbled in text as 42 ½0).

AI explanation

Using the clock angle formula, the angle between the hands equals the absolute value of 30 times the hours minus 11 divided by 2 times the minutes. Substituting the values gives 30 times 5 minus 5.5 times 35, which is 150 minus 192.5. The absolute value of negative 42.5 is 42.5 degrees.

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