Answer
36$^{\circ}$
Work Step by Step
1. A star has radical symmetry, so if you look at the pink angle labeled as $2\theta$, you will see that five of those fit into the 360$^{\circ} $of the circle:
$360^{\circ}\div5=72^{\circ}$
2. If $2\theta=72^{\circ}$ then $\theta=36^{\circ}$
