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The problem does not mention that the arc is intercepted by the central angle (an angle where the vertex is the center point of the circle).

I'll assume that it is, based on the given data.

Measure of central angle = measure in degrees of the intercepted arc.

So the formula for arc length is:

arc length = central angle × circumference
                   360 degrees

Let X be the central angle

6.28 cm =     X     × 37.68 cm

6.28 cm (360 °) = X (37.68 cm.)
  37.68 cm              37.68 cm

2,260.8 (cm) (degrees) = X
    37.68 cm
       60 degrees = X

The central angle is 60 degrees.

measure of central angle = degree measure of the arc intercepted

Degree measure of the arc = 60 degrees

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Use this formula: A/360 = 6.28/37.68. second step: you cross multiply in order to arrive on this equation: 37.86 A = 2260.8.
Third step: divide both sides by 37.68.
The answer would be 60.
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