The aim of this study is calculation of bifurcation carotid angle by detection of vessel boundaries to assist the medical doctors if this angle is a risk factor about formation of carotid plaques.Carotid ct angiography images are clustered automatically by ISODATA unsupervised classification algorithm. Since the spectral digital numbers (DN) of vessel pixels are bigger than the other part of the images, the cluster which has the biggest median value of DN among all other classes gives the vessel class. The cluster image in raster format is converted into the vector format which allows working on the vessel geometry. The converted vector vessel cluster dataset has been simplified using Douglas-Peucker algorithm to eliminate the zigzag effects of pixel data which are remained on the vector form dataset. Then the cluster polygon is converted to lines and the vertices which will be used for the calculation of bifurcation carotid angle. For sorting the vertex points to calculate the angle on each vertex, alpha-shapes algorithm is applied along the boundary. Then all the angles on each vertex point along the boundary of vessels are calculated. It is also visually clear that the angle which has the minimum value among all the calculated angles, gives the bifurcation carotid angle for one projected plane. The final carotid angle has calculated and 18 sample datasets are used to test the method.