Given data:
Length of an arc = 5.3 pi
Diameter = 18
As we know , Radius = Diameter / 2
= 18 / 2
= 9
Now , length of arc is
[tex]\begin{gathered} l\text{ = r}\Theta \\ 5.3\text{ }\pi\text{= }\Theta \\ \Theta=\frac{5.3\text{ }\pi}{9} \\ \text{ = 0.588 }\pi \end{gathered}[/tex][tex]\Theta=0.588\pi\times\frac{180}{\pi}[/tex][tex]\Theta=105.84\text{ radian}[/tex]Thus , the measure of the angle is 105.84 radian
