A couple of math questions...?

Question

1. Why is a circle 360 degrees?

2. Why do we typically measure angles from right to left on a protractor?

Answer 1

60 and 460 were common values to use in the ancient world -- particularly by the Babilonians. The main reason is that it is easily divided into parts. 60 is divisible by 2, 3, 4, 5 and 6.

It is the same reason why we use 60 second to a minute, 60 minutes to an hour and 3600 seconds to an hour.

Your second question has a more modern answer. We now tend to look at angles that use the Origin of the Cartesian plane as one edge and a straight line starting from the origin as the other edge. If the protractor is set up with the center of the straight edge on the origin & the straight edge lined up on the X-Axis -- then the lower angles will be in the first quadrant. and angles above 90 degrees will be in the second quadrant.

Answer 2

Because there are 360 degrees in a circle. If you draw a circle with centre 0,0 and radius 1 unit. You have the unit circle. The x and y axes divide this circle into 4 sections of angles 90 degrees. 4 by 90 = 360

Because you're meauring from + 0, the x axis. It's convention

Answer 3

These are just some definitions adopted by some old Greek so mathematics could be taught in a logical matter and everyone would get the same answers. you could just as easily defined a circle as 400 degrees but the sines, cosines and tangents would have to be recalculated. we commonly use a 2pi radians for the angular measure of a circle and military gunnery uses 6400 mils. it is jus the adoption of a standard.

with regard to question 2 this is just a matter of definition to keep everyone on the same page. the early mathematicians just deceide that they would call a counterclockwise angle positive and everyone adopted it for the sake of uniformity.

These questions are about as meaningful as asking why do we call a tree a tree?