Determine the degree measure of an arc with the given length, L, in a circle with the given radius, r.?

if the radius is 100, then what is the circumference, i.e. the length around the circle? its 2*pi*radius=200*pi. So, now we take a ratio of the length L to the entire length of the circle, so we have 20/(200pi)=1/(10pi) thus, we have gone around 1/10pi of the circle. So multiply this by 360 degrees, (or 2pi radians) to get the degree(or the radian) angle measure

The length (L) swept out by a rotation of an angle (θ) measured in radians with radius (r) is:

L = rθ

Solving for θ:

θ = L/r

To convert from radians (θ) to degrees (x) use

x = (180/π)θ

Therefore, the angle in degrees is:

x = (180/π)(L/r)

x = (180/π)(20/100)

x ≈ 11.46°

x = angle measure in radians

Then L = rx

x = L/r = 20/100 = .2 radians

x = 11.46 degrees