If a clock shows 6:00, what is the angle between the hour and minute hands?

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Question: If a clock shows 6:00, what is the angle between the hour and minute hands?

Options:

Correct Answer: 180 degrees

Solution:

At 6:00, the hour hand is at 180 degrees and the minute hand is at 0 degrees. The angle between them is |180 - 0| = 180 degrees.

If a clock shows 6:00, what is the angle between the hour and minute hands?

If a clock shows 6:00, what is the angle between the hour and minute hands?

Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
Step 2: At 6:00, the hour hand points directly at the 6 on the clock.
Step 3: The clock is a circle, and each number on the clock represents a position in degrees.
Step 4: The full circle of the clock is 360 degrees.
Step 5: Each hour on the clock represents 30 degrees (360 degrees divided by 12 hours).
Step 6: Since the hour hand is at 6, we calculate its position: 6 hours x 30 degrees/hour = 180 degrees.
Step 7: At 6:00, the minute hand points at the 12 on the clock, which is 0 degrees.
Step 8: To find the angle between the hour and minute hands, subtract the smaller angle from the larger angle: |180 degrees - 0 degrees|.
Step 9: Calculate the difference: |180 - 0| = 180 degrees.
Step 10: The angle between the hour and minute hands at 6:00 is 180 degrees.

Clock Angles – Understanding how to calculate the angle between the hour and minute hands of a clock based on their positions.