jmc

Taking one exterior angle per vertex, the sum of the exterior angles of a polygon is $360^{\circ }$. If each exterior angle is $30^{\circ }$, then the polygon has $\frac{360}{30}=12$ sides. The sum of the interior angles of an $n$-sided polygon is $180(n-2)$, so for a polygon with 12 sides, the sum of the interior angles is $180(12-2)=\boxed{1800}$ degrees.