Of course, if you put a dot inside (i.e., not touching any side) any shape and extend a ray from it, you can spin it around 360 degrees. The problem as posited is that what's being asked is implicitly inconsistent. Interior angles, sure: 180 (sides-2) and the reason for that is obvious by inspection. Circle: trick part, which queers the entire question. It doesn't test mathematical ability, other than having the skill to call foul on it. [I wrote something else, but I don't know who the audience is here....]
Of course, if you put a dot inside (i.e., not touching any side) any shape and extend a ray from it, you can spin it around 360 degrees. The problem as posited is that what's being asked is implicitly inconsistent. Interior angles, sure: 180 (sides-2) and the reason for that is obvious by inspection. Circle: trick part, which queers the entire question. It doesn't test mathematical ability, other than having the skill to call foul on it. [I wrote something else, but I don't know who the audience is here....]