for a circle with a radius of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 5/2 pi meters

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi r\theta }{180}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=6\\ s=\frac{5\pi }{2} \end{cases}\implies \cfrac{5\pi }{2}=\cfrac{\pi \cdot 6\cdot \theta }{180}\implies \cfrac{5\pi }{2}=\cfrac{\pi \theta }{30} \\\\\\ \cfrac{5\underline{\pi }\cdot 30}{2\underline{\pi} }=\theta \implies 75=\theta[/tex]