## University Calculus: Early Transcendentals (3rd Edition)

The angle is $\frac{5\pi}{4}$ in radians and $225^\circ$ in degrees.
To find out the angle, we need to employ the formula: $$s = r\theta$$ which means $$\theta=\frac{s}{r}$$ $s$: the length of the arc $r$: radius of the circle $\theta$: the central angle of the arc (in radians) Here $r = 8$ and $s=10\pi$ So the angle would be (in radians): $$\theta=\frac{10\pi}{8}=\frac{5\pi}{4}$$ In degrees, that angle would be: $$\theta=\frac{5\pi}{4}\times\frac{180^\circ}{\pi}=\frac{5\times180^\circ}{4}=225^\circ$$