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Find the angle between the minute hand and the hour hand of a clock at 1) 4:30PM and 2)10:40 PM?
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Find the angle between the minute hand and the hour hand of a clock at...
Angle between the Minute Hand and Hour Hand of a Clock

Case 1: 4:30 PM

  • At 4:30 PM, the hour hand is pointing directly at the 4 and the minute hand is pointing at the 6.

  • The angle between the hour hand and the 12 o'clock mark is 4 x 30 = 120 degrees.

  • The angle between the minute hand and the 12 o'clock mark is 6 x 30 = 180 degrees.

  • Since the minute hand is ahead of the hour hand, we need to find the difference between the two angles.

  • The angle between the minute hand and the hour hand is 180 - 120 = 60 degrees.



Case 2: 10:40 PM

  • At 10:40 PM, the hour hand is pointing between the 10 and the 11 and the minute hand is pointing at the 8.

  • The angle between the hour hand and the 12 o'clock mark is 10 x 30 + 40 / 2 = 310 degrees.

  • The angle between the minute hand and the 12 o'clock mark is 8 x 30 = 240 degrees.

  • Since the hour hand is slightly past the 10 and the minute hand is before the 12, we need to add 360 degrees to the angle of the hour hand.

  • The angle between the minute hand and the hour hand is 240 - (310 + 360) = -430 degrees.

  • Since we want a positive angle, we add 360 degrees to get the final answer.

  • The angle between the minute hand and the hour hand is 360 - 430 = 70 degrees.



Conclusion: The angle between the minute hand and the hour hand of a clock at 4:30 PM is 60 degrees and at 10:40 PM is 70 degrees.
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Find the angle between the minute hand and the hour hand of a clock at...
Formula:|5.5*min-30*h| ,1)45,2)80
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Find the angle between the minute hand and the hour hand of a clock at 1) 4:30PM and 2)10:40 PM?
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