Answer: The formula for the length of an arc is L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle of the arc in radians.
To solve this problem, we need to convert the measure of the central angle from degrees to radians. Since 360 degrees is equal to 2π radians, we have:
125 degrees = (125/360) * 2π radians
125 degrees = (5/18) * π radians
So, the central angle θ is (5/18) * π radians, and the length of arc RS is given as:
L = (25π/9)
Now we can use the formula for arc length to find the radius r:
L = rθ
(25π/9) = r * (5/18)π
r = (25π/9) / (5/18)π
r = (25/9) * (18/5)
r = 5 * 6
r = 30
Therefore, the radius of the circle is 30 units.
Explanation: