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Please look at this question

https://math.stackexchange.com/posts/comments/9011243?noredirect=1

A user comment this so I thought of asking here

You mean why did we decide on using 360 degrees? I don't know for sure, but question would probably belong on hsm.stackexchange.com. I assume the reason is because 360 is highly composite, which also explains why the clock has 12 hours. – Elliot G 1 hour ago

Another user comment it

Babylonian scholars liked the number 360 because it has many divisors, and from there it became popular in antiquity (also because a few easily constructible angles have integer measure). An alternative system where the right angle is 100 degrees (the so-called centesimal degree) was proposed by revolutionary French academics, but it barely spread ouside of some surviving niche. In my opinion presenting degrees (sexagesimal or otherwise) as anything more than a celebrated relic which has many practical uses is a distortion of our current understanding of angles, which is radians. – Saucy O'Path

So basically that 1st user comment has stated my question " why we took a whole round or circle into 360 parts only naming each part angle as 1° not a circle with parts 540 , 260 etc etc.. only 360??

2nd user said it due to Babylonian history

Can you explain it history of dividing circle in 360° only??

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A full circle is assigned 360 degrees because the Babylonians and the Sumerians used the sexagesimal (base-60) system of counting. As discussed in an article on Wonder Quest, this, in turn, had come from their observation of the Sun completing a complete circle around the Earth in about 360 days:

The Sumerians watched the Sun, Moon, and the five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn), primarily for omens. They did not try to understand the motions physically. They did, however, notice the circular track of the Sun's annual path across the sky and knew that it took about 360 days to complete one year's circuit. 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.

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