I have a problem that goes like this:
"In a circle with radius $6$, what is the measure (in degrees) of an arc whose length is $2\pi$?"
I thought that the answer would be $360$ degrees because $2\pi$ radians is one circle, but the answer in the book is $60$ degrees. The book solved it like this:
$$Circumference=2\pi r=12\pi$$ $2\pi$ is $1/6$ of the circumference: $$1/6\times360=60$$ This route makes sense to me, but I am really confused on the part that it said the length of the arc was $2\pi$, and $2\pi$ radians is $360$ degrees. I drew the conclusion that it meant radians because I was told that you assume that a measure is in radians unless you are told that it is something else. I have just learned about radians, and I obviously made a mistake. Can someone explain to me where I went wrong?