Let [tex]L[/tex] be the length of an arc subtended by an angle of [tex]\theta[/tex] on a circle of radius [tex]r[/tex]. Then the ratio of the arc's length to its subtended angle is proportional with the circle's entire circumference to one complete revolution:
[tex]\dfrac{2\pi r}{2\pi}=\dfrac{L}{\theta}[/tex]
Solving for [tex]L[/tex] yields the formula for arc length of a circular arc,
[tex]L=r\theta[/tex]
where [tex]\theta[/tex] is in radians. To convert to degrees, use the conversion factor [tex]\dfrac{180^\circ}{\pi\text{ rad}}[/tex].
[tex]L=4\times\left(72^\circ\times\dfrac{\pi\text{ rad}}{180^\circ}\right)=4\times\dfrac{2\pi}5=\dfrac{8\pi}5\approx5.0265[/tex]
