Answer: The arc length, the radius, and the central angle of a circle are related by the formula:
arc length = radius x central angle
Therefore, we can find the central angle by dividing the arc length by the radius:
central angle = arc length / radius
In this case, the arc length is 30π units and the radius is 20 units, so:
central angle = (30π units) / (20 units) = 3π / 2 radians
This is the measure of the central angle in radians. In degrees, we can convert this angle by multiplying by 180/π:
central angle = (3π / 2 radians) x (180/π degrees per radian) ≈ 270 degrees
Therefore, without calculating, I think the measure of the central angle is approximately 270 degrees. This is because the arc length is more than three-quarters of the circumference of the circle (which has a circumference of 2πr = 40π units), so the central angle should be more than three-quarters of a full circle, which is 270 degrees.
Explanation: