If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc?

I guess what you are asking is what is the measure of the central angle?

arc length = radius * central angle (in radians)

central angle (in radians) = arc length / radius

central angle (in radians) = 12 / 10

central angle (in radians) = 1.2 radians = 68.7549 degrees