Why is a full turn of the circle 360°? Why not any other number? I was just wondering why we have 90° degrees for a perpendicular angle. Why not 100° or any other number?
What is the significance of 90° for the perpendicular or 360° for a circle?
I didn't ever think about this during my school time.
Can someone please explain it mathematically? Is it due to some historical reason?

It is from ancient astronomy. A day in earth is a natural unit of time, and one year is also a natural time unit. one year is 360 days in ancient calendar,  People related to circle to year, therefore a circle is divided to 360 degrees. There is not much free choices here if we establish this relationship. 
The accepted answer can explain why people choose 360 over 365, but cannot explain why a circle is not 720 or 3600. 
