Given:
Arc length = 8 inches
radius = 3 inches
find the measure of the central angle.
Arc length = radius * central angle
central angle = arc length / radius
central angle = 8 inches / 3 inches
central angle = 2.667 (radian)
Central angle in degrees = 152.88°
Circumference of the circle = 2 * 3.14 * 3 inches = 18.84 inches
1 circle = 360° / 18.84 inches = 19.11° per inch
19.11° per inches * 8 inches of arc length = 152.88°
