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Time, Clock & Calendar Hard 3 min

What is the smaller angle between the hour and minute hands of a clock at exactly 5:40?

Hint
The hour hand moves continuously; it is not exactly on 5.

Answer

70 degrees.

Explanation

At 5:40, the minute hand is at 240 degrees. The hour hand is at 5 × 30 + 40 × 0.5 = 170 degrees. The difference is 70 degrees.

Step-by-Step Solution

Minute hand = 40 × 6 = 240°.
Hour hand = 5 × 30 + 40 × 0.5 = 170°.
Difference = 240 - 170 = 70°.
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