SOLUTION: What is the number of degrees in the smaller angle formed by the hands of a clock at $8:55$?

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Question 1205037: What is the number of degrees in the smaller angle formed by the hands of a clock at $8:55$?
Found 3 solutions by MathLover1, ikleyn, math_tutor2020:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


we can calculate the angle using the following formula

where =minutes and =hours
in your case and

degrees
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
What is the number of degrees in the smaller angle formed by the hands of a clock at 8:55 ?
~~~~~~~~~~~~~~~~~~~~~~~~ 

The angular rate of rotation of the hour hand is 360 degrees in 12 hours, 

    or   = 30 degrees per hour =  = 0.5 degree per minute.


The angular rate of rotation of the minute hand is 360 degrees in 1 hour, or  = 6 degrees per minute.


At 8:55, the greater angle of the minute hand with the position 12:00 o'clock is 6*55 = 330 degrees.

         the greater angle of the hour hand with the position 12:00 o'clock is 8*30 + 55*0.5 = 267.5 degrees.


Your answer is the difference  330 - 267.5 = 62.5 degrees.

Solved, with explanations.

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To see many other similar  (and different)  problems on angles between clock hands,  look into the lessons
    - Clock problems
    - Advanced clock problems
in this site.

Learn the subject and the method from there.

------------------

The meaning of this task is not to take / (to find) a formula ready to use and plug in the numbers.

The meaning is to deduce the necessary formulas and to learn and to understand on HOW TO do it.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Analog clocks seem to be an ancient relic at this point (when compared to modern digital clocks), but I recommend seeing if you can find one laying around your house somewhere.

If you don't have a physical clock then there's always a simulation of one such as this interactive clock
https://www.visnos.com/demos/clock
Feel free to play around with the various settings. Other similar clocks can be found online.

I recommend using that tool to check your work rather than do your work for you.
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