What is the measure of the smaller angle formed by the hour hand and the minute hand of a clock at 2:00?

Rationale

The measure of the smaller angle formed by the hour hand and the minute hand of a clock at 2:00 is 60 degrees.

At 2:00, the hour hand is positioned at the 2, while the minute hand points at the 12. Each hour mark on the clock represents 30 degrees (360 degrees divided by 12 hours), resulting in a 60-degree angle between the two hands.

A (40 degrees) YOUR ANSWER

A 40-degree angle would imply that the hour hand is slightly ahead of the 2 o'clock position, which is not the case at 2:00. The actual positions of the hands make the angle much larger than 40 degrees, as the hour hand is directly on the 2.

B (45 degrees) YOUR ANSWER

A 45-degree angle suggests that the hour hand is positioned between the 2 and the 3. However, at exactly 2:00, the hour hand is precisely aligned with the 2, and thus the angle formed with the minute hand at 12 is clearly larger than 45 degrees.

C (50 degrees) YOUR ANSWER

A 50-degree angle is also incorrect, as it would require the hour hand to be positioned slightly before the 2 o'clock mark. The clear hour hand position at 2:00 indicates that the angle is definitively larger than 50 degrees.

D (60 degrees) CORRECT

This choice correctly represents the angle formed at 2:00, calculated as two hour marks apart on the clock (2 and 12), which results in a 60-degree angle (2 hours × 30 degrees/hour = 60 degrees).

E (90 degrees) YOUR ANSWER

A 90-degree angle would mean that the hands are perpendicular, which is not true at 2:00. The hour hand is at 2 and the minute hand at 12, making the angle between them 60 degrees, not 90.

Conclusion

At 2:00, the angle between the hour and minute hands of a clock is correctly measured as 60 degrees. This is determined by the positions of the hands, where the hour hand at 2 and the minute hand at 12 create an angle that is consistent with the hour-mark spacing of the clock. All other options misrepresent the angle formed at this specific time.

What is the measure of the smaller angle formed by the hour hand and the minute hand of a clock at 2:00?

The measure of the smaller angle formed by the hour hand and the minute hand of a clock at 2:00 is 60 degrees.

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