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It's just a convention. Mathemeticians could have chosen some other number, but 360 is divisible by many whole numbers, so it is convenient.
It has some interesting history behind. Sumerians of Mesopotamia observed the sun, moon and other planets.
They noticed that the circular track of the Sun's annual path across the sky and found that it took about 360 day-nights to complete one circle.
Consequently, they divided the circular path into 360 degrees to track each day's passage of the Sun's whole journey.
This probably happened about 2400 BC.
Beyond that, the number 360 has some interesting facts.
It is the number divisible by all numbers from 1 to 10 except 7 and has more factors.
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What is 35 percent of 360 degrees?
35% of 360 degrees = 35% * 360 = 0.35 * 360 = 126 degrees
How many degrees does a rectangle to add to?
all the angles are right angles (90 degrees) and add to 360 degrees
How many degrees in a circle?
360 degrees are in a circle no matter how big or small the circle is A circle has 360 degrees.
What is one third of 360 in degrees?
It is: 1/3 of 360 degrees = 120 degrees
What is one eights of 360 degrees?
It is: 1/8 of 360 degrees = 45 degrees
