Finding the Smallest Angle in a Dodecagon

Consider a polygon that consists of 12 sides (a dodecagon). The interior angles of a polygon can be calculated using the formula:

$$ S = (n - 2) \times 180 $$

where $$ S $$ is the sum of the interior angles and $$ n $$ is the number of sides of the polygon.

If one of the interior angles of this dodecagon is twice as large as the smallest angle in the polygon, what is the measure of the smallest angle?