Multiple choice

When the time in a clock is 4:30 A.M., then the angle between the hands of the clock is A° and when the time in the clock is 5:50 A.M., then the angle between the hands of the clock is B°. Find the value of (B° – A°).

  1. 60°

  2. 75°

  3. 56°

  4. 80°

  5. 67°
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D Correct answer
Explanation

Angle formula: |30H - 5.5M|. For 4:30, |30(4) - 5.5(30)| = |120 - 165| = 45. For 5:50, |30(5) - 5.5(50)| = |150 - 275| = 125. B - A = 125 - 45 = 80.

AI explanation

Using the clock angle formula of 30 times the hours minus 5.5 times the minutes, the angle A at 4:30 is calculated as 120 minus 165, resulting in an absolute value of 45 degrees. The angle B at 5:50 is calculated as 150 minus 275, resulting in an absolute value of 125 degrees. The difference between B and A is 125 minus 45, which equals 80 degrees. The result is 80 degrees.

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