What is the angle between the two hands of a clock at 12, 2:00, and 2:30

Dear Student,

Please find below the solution to the asked query :
At 12 both will coincides so angle is 0.
At 2 O' clock angle is 60 degree.
At 2:30 angle is :
At 2:30 pm, the hour hand will be halfway between the 2 and the 3. 

Every 12 hours, the hand makes a full 360-degree revolution. So in 2.5 hours, it goes 2.5 times 360 / 12 = 75 degrees.

Every hour, the hour hand travels 360/12 = 30 degrees. Time t is measured in hours, according to the first sentence, so at time t, the hour hand is at 30t degrees. 

Every hour, the minute hand travels a full 360 degrees, so at time t, the minute hand is at 360t. 


The tricky bit with the last part is that you have to do modulus arithmetic. Subtract off the 720 degrees that the minute hand has already traveled, and just focus on where it is on this revolution. 

m=360t-720 
h=30t 

So for h and m to be the same, 30t must equal 360t-720 
360t-720=30t 
330t=720 
11t = 24 
t = 24/11 
The angle will therefore be 30 times 24/11 = 720/11, or 65 5/11 degrees. 



Hope this would clear your doubt about the topic.

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Regards

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