We use DEGREES to measure parts of circles.  Degrees were created many years ago and have stuck around since.

Degrees are not the only way to measure inside circles. We can also use the length of the radius as a measuring tool.  Imagine a circle made of string lying on a surface.  We can take a radius-length piece of string and lay it along the outside of the circle, like shown below.  It will fit along the circumference just over six times. (please pardon my poor mouse drawing skills)

Actually, it fits 6.28318... times! You will also hear this number stated as "2p".  Now you know why you have that pi button on your calculator!
Look at the 6 full slices above. Each slice is called one "radian" and the angle of each slice at the middle is about 57.3 degrees.

We will often refer to the angle made by any two radii as "theta", or just q.  When the arc length (often called "s") equals the radius length, the angle q is exactly one radian.
NOTE: Many physics books would repeat what I just said like this: "When the angle subtended by an arc length "s" exactly equals the radius length, the angle theta is exactly one radian."

Here is a website that will convert all the circular measures if you are too lazy to do it yourself.
Here's another site that gives more background about circles.  Please let me know if these links do not work!

All of the uniform motion and acceleration equations stated before also work with circles.
Replace degrees with "q", called theta and is in radian
Replace the "a" with "a", called alpa and is in radians/sec/sec.
Replace "V" with "w", called omega and is in radians/sec.

wf=wo+at
Dq=wt+at²/2
wf²=wo²+2aq
Click here, login and solve these 4 problems: "circle motion", "radians",  "convert to radians", and "circle displacement".