Given that
Radius = 5
[tex]\begin{gathered} \text{Length of the arc is betw}e\text{n 2}\pi\text{ and 3}\pi \\ \text{Length of the arc = }\frac{\theta}{360}\text{ x 2}\pi r \\ \text{Where }\theta\text{ = x} \\ \text{For L = 2}\pi \\ 2\pi\text{ = }\frac{x}{360\text{ }}\text{ x 2}\pi\text{ x 5} \\ 2\pi\text{ = }\frac{x\cdot\text{ 10}\pi}{360} \\ \text{Cross multiply} \\ 360\cdot\text{ 2}\pi\text{ = 10}\pi x \\ \text{Isolate x} \\ x\text{ = }\frac{720\pi}{10\pi} \\ x=72^o \\ \text{For 3}\pi \\ 3\pi\text{ = }\frac{x}{360}\text{ x 2}\pi\cdot\text{ 5} \\ 3\pi\text{ = }\frac{10\pi x}{360} \\ \text{Cross multiply} \\ 3\pi\text{ x 360 = 10}\pi x \\ \text{Isolate x} \\ \text{x = }\frac{1080\pi}{10} \\ \text{x = 108}^o \end{gathered}[/tex]
Therefore, x can either be 72 or 108 degrees
The lowest possible integer is 72
