The length of an arc is given as:
[tex]l=\frac{\theta}{360}\times2\pi r[/tex]However, we don't seek "l" because it is already given. Our approach is to make the angle we seek the subject of the formula.
Given:
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \text{ We multiply 360 to both sides to get:} \\ 360l=\theta\times2\pi r \\ \text{ We divide both sides by 2}\pi r\text{ to get} \\ \frac{360l}{2\pi r}=\theta \end{gathered}[/tex]The angle is therefore:
[tex]\theta=\frac{360\times7}{2\pi\times12}=33.42^o[/tex]The angle subtended is 33.42 degrees
