EXPLANATION
We are given the following parameters:
Length of arc= 5/3pi
Diameter = 18 feet
Therefore, radius =18/2 = 9 feets
The formula for the length of the arc is given below.
[tex]\text{length of arc =}\frac{\theta}{360}\times2\pi r^{}[/tex]We will substitute the given parameters into the formula above to get the measure of the angle.
[tex]\begin{gathered} \frac{5}{3}\pi=\frac{\theta}{360}2\pi\times9^{} \\ \frac{5}{3}\pi=\frac{18\theta}{360}\pi \\ crossmultiply\text{ } \\ 3\times18\theta\pi=360\times5\pi \\ 54\theta\pi=1800\pi \\ \text{Divide both sides by 54}\pi \\ \theta=\frac{1800\pi}{54\pi} \\ \theta=33.3^0 \end{gathered}[/tex]Therefore, the measure of the angle is
[tex]\theta=33.3^0[/tex]