Before revision: The dualistic structure of statistical manifolds  yields eight types of geodesic triangles defining overall eighteen interior angles. In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis  geometry, or exhibit either angle excesses or angle defects.
After revision: The dualistic structure of statistical manifolds yields eight types of geodesic triangles passing through three given points, the triangle vertices. The interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis geometry, or exhibit either angle excesses or angle defects.