What is the measure of the smaller angle formed by the hour and minute hand of a clock at 4:00?

Rationale

The measure of the smaller angle formed by the hour and minute hand of a clock at 4:00 is 120 degrees.

At 4:00, the hour hand points at the 4, while the minute hand points at the 12. Each hour on the clock represents 30 degrees (360 degrees / 12 hours), so the angle between the hour hand and the minute hand at this time is 4 hours * 30 degrees/hour = 120 degrees.

A (90 deg) YOUR ANSWER

A 90-degree angle would imply the hour and minute hands are perpendicular to each other. At 4:00, the minute hand is at 12 and the hour hand at 4, which creates a much larger angle of 120 degrees rather than 90 degrees.

B (120 deg) CORRECT

This choice correctly identifies the angle formed by the hour hand at 4 and the minute hand at 12. Given that each hour represents 30 degrees and the hour hand is at 4, the angle is calculated as 4 * 30 = 120 degrees.

C (130 deg) YOUR ANSWER

An angle of 130 degrees would suggest a position between the hour and minute hands that does not occur at 4:00. The actual angle is less than this, as the hour hand is positioned at 120 degrees relative to the 12 o'clock position.

D (135 deg) YOUR ANSWER

Similar to option C, a 135-degree angle would place the hour and minute hands in a configuration that does not align with the positions at 4:00. The calculated angle is 120 degrees, making this choice incorrect.

Conclusion

The smaller angle formed by the clock hands at 4:00 measures 120 degrees, as determined by the positions of the hour and minute hands. Other options misrepresent the angular relationship, highlighting the importance of understanding how time correlates with degrees on a clock face. This precise calculation illustrates fundamental principles of geometry applied in everyday contexts.

What is the measure of the smaller angle formed by the hour and minute hand of a clock at 4:00?

The measure of the smaller angle formed by the hour and minute hand of a clock at 4:00 is 120 degrees.

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