We can calculate the measure of the angle theta by the arc length formula:
[tex]\text{Arc length= 2}\pi r(\frac{\theta}{360})[/tex]
Substituing in the formula:
[tex]\begin{gathered} 6=2\pi(4)(\frac{\theta}{360}) \\ \text{Isolating the variable }\theta\colon \\ \theta=\frac{6\cdot360}{2\pi\cdot4} \\ \theta=85.94\text{ degrees} \end{gathered}[/tex]
To convert the angle to radians:
[tex]\begin{gathered} \theta\cdot\frac{\pi}{180}=x\text{ rad} \\ 85.94\cdot\frac{\pi}{180}=1.5\text{ rad} \end{gathered}[/tex]
