Okay, who knows Geometry?

I have a dodecagon (12 sides) and because there are 12 vertices extending from the center of the dodecagon at equidistant points, that means that each angle is 30 degrees (30 * 12 sides = 360 degrees).

If the outer area with the lines (vertices) come to are congruent lines (in length) and you have other parallel lines going around the 12 sides at equidistant points from the center to the outer edge, and those lines are all parallel, then how do you figure out those inner angles near the outer area? My challenge is in how to explain what I am looking for.

Cecil