An arc of a circle has a length of 4pi units. If the circle it comes from has a radius of 12 units, what is the measure of the central angle in radians associated with this arc? NO LINKS PLEASE

If we start with a circle with a marked radius line, and turn the circle a bit, the area marked off looks something like a wedge of pie or a slice of pizza; this is called a "sector" of the circle, and the sector looks like the green portion of this picture:

circle with central angle "θ" and radius "r" marked, delineating the sector, which is shaded a light green

The angle marked off by the original and final locations of the radius line (that is, the angle at the center of the pie / pizza) is the "subtended" angle of the sector. This angle can also be referred to as the "central" angle of the sector. In the picture above, the central angle is labelled as "θ" (which is pronounced as "THAY-tuh").

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