Capping Shadow Volumes - Fast Angle detection?


I am trying to cap my shadow volumes using some triangulation allgorithm, from the silhouette polygon, I would like to detect convex and concave vertices. ie all vertices in the silhouette contour with an interior angle < 180 is a convex vertex, Now my question is, Is there a fast way to detect angles between two vectors in 3d? Something like Fowler angles in 3d?, Currently, I am using the scalar triple product between the two edge vectors from the silhouette and the silhouette plane normal, This does work but I would like to know if there is a way to determine angles without doing a triple product? coz all i am ineterested is if the angle is greater than 180 degrees or not.

Thanks in advance,