Explanation
The formula to find the arc length of a circle if the angle is measured in degrees is:
[tex]\text{ Arc length }=\frac{\theta}{360°}\cdot2\pi r[/tex]
In this case, have:
[tex]\begin{gathered} \theta=x \\ r=8in \\ \text{ Arc length }=18in \end{gathered}[/tex]
Now, we substitute the know values in the arc length formula and solve for x:
[tex]\begin{gathered} \text{ Arc length }=\frac{\theta}{360°}\cdot2\pi r \\ 18in=\frac{x}{360°}\cdot2\pi(8in) \\ 18in=\frac{x}{360\degree}\cdot16\pi in \\ \text{ Multiply by 360\degree from both sides} \\ 360\degree\cdot18\imaginaryI n=360\degree\cdot\frac{x}{360\operatorname{\degree}}\cdot16\pi\imaginaryI n \\ 360\degree\cdot18\mathrm{i}n=16\pi xin \\ \text{ Divide by }16\pi in\text{ from both sides} \\ \frac{\begin{equation*}360\degree\cdot18\mathrm{i}n\end{equation*}}{16\pi in}=\frac{16\pi xin}{16\pi in} \\ \frac{6480\degree}{16\pi}=x \\ 128.9\degree\approx x \\ \text{ The symbol }\approx\text{ is read 'approximately'.} \end{gathered}[/tex]Answer
The measure of the angle x rounded to the nearest tenth is 128.9°.
