Why is a full circle 360 degrees? Why not just a round number like 100 or any other number?

Answer 1

The Egyptians figured out a long time ago that years ran in cycles of about 360 days. Thus, calendars (some of which used the sun as a guide) used circles divided up into 360 parts. Also, the numbers 360 and 60 are divisible by so many other numbers that they proved convenient and have stood up over the centuries.

Your suggestion of 100 is not a bad one as the universal acceptance (outside the US) of the metric system attests, but 100 doesn't have the analogues in nature that 360 does.