Problem 2 · 1999 AMC 8
Easy
Geometry & Measurement
angle-measure
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
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Answer: C — 60°.
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Hint 1 of 2
A clock face is just a circle cut into 12 equal slices. Forget degrees for a moment — how many slices sit between the 10 and the 12?
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Hint 2 of 2
Each hour-slice is the same size: 360° ÷ 12 = 30°. Count the slices, then multiply.
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Approach: the clock is 12 equal 30° slices — count slices
- At exactly 10 o'clock the hour hand is on the 10 and the minute hand is on the 12. There are two number-gaps between them (10→11→12).
- Each gap is one-twelfth of the full turn: 360° ÷ 12 = 30°. Two gaps give 2 × 30° = 60°.
- You'll see it again: any "angle between clock hands on the hour" is just (number of gaps) × 30°. Knowing the 30°-per-hour grid makes every on-the-hour clock angle instant.
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