To determine which two different times could create a 60° angle between the hour and minute hands of a clock, we can evaluate the options given.
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2:00 and 10:00:
- At 2:00, the hour hand is at 60° and the minute hand is at 0°, making the angle 60°.
- At 10:00, the hour hand is at 300° and the minute hand at 0°, making the angle 300° (or equivalently 60° since 360° - 300° = 60°).
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3:00 and 9:00:
- At 3:00, the hour hand is at 90°, and the minute hand is at 0°, making the angle 90°.
- At 9:00, the hour hand is at 270°, and the minute hand at 0°, making the angle 270° (not 60°).
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4:00 and 8:00:
- At 4:00, the hour hand is at 120°, and the minute hand is at 0°, making the angle 120°.
- At 8:00, the hour hand is at 240°, and the minute hand at 0°, making the angle 240° (not 60°).
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6:00 and 12:00:
- At 6:00, the hour hand is at 180°, and the minute hand is at 0°, making the angle 180°.
- At 12:00, the hour hand is at 0°, and the minute hand at 0°, making the angle 0°.
The only pair that gives a 60° angle in both cases is the first pair:
2:00 and 10:00.