Minimum angle at points for every possible polygon

Question

Given a point set $S$ in 2-dimensional space, one can generate a multitude of possible polygons with a vertex at each point $s_i \in S$. I'm working on the problem of finding such a polygon with minimal/maximal area. I'm interested if you someone knows how to compute a lower bound for the inner angle at a specific point in $S$. By the inner angle I mean the angle which is completely inside the polygon. Obviously $0 < \alpha < 360$, because the point has to be one of the polygons vertices and may not lay inside the polygon. I can imagine that for a given instance, some vertices separate the point set and therefore need a certain inner angle to do so. Of course for my case it might help if you consider the polygon to be of maximum or minimum area.