Multiple choice

At 20 minutes past 4 in the afternoon (4:20), what is the reflex angle between the hour hand and the minute hand of a clock?

  1. 350°

  2. 10°

  3. 120°

  4. 130°

  5. 100°
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A Correct answer
Explanation

At 4:20, the hour hand is at 4 + 20/60 = 4.33 hours. The angle from 12 is 4.33 * 30 = 130 degrees. The minute hand is at 20 minutes, which is 20 * 6 = 120 degrees. The angle between them is |130 - 120| = 10 degrees. The reflex angle is 360 - 10 = 350 degrees.

AI explanation

At 4:20, the hour hand is at (4 x 30) + (20 x 0.5) = 130 degrees and the minute hand is at 20 x 6 = 120 degrees. The smaller angle between them is 130 - 120 = 10 degrees. The reflex angle is the outer angle, so subtract this from 360 degrees: 360 - 10 = 350 degrees.

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