Answer
$\dfrac{13 \pi}{5} \ in.=2.6 \pi \ in.$
Work Step by Step
$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$
or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$
Here, $r$ represents radius and $d$ is diameter.
We are given that the red arc measures $180^{\circ}-50^{\circ}=130^{\circ}$ and $d=7.2 \ in.$
Thus, equation (b) becomes:
$l=\dfrac{130^{\circ}}{360^{\circ}} \times \pi (7.2)=
\dfrac{13 \pi}{5} \ in.=2.6 \pi \ in.$
