# Total number of non similar triangles which can be formed such that all the angles of the triangles are integers

My question is: " Find the total number of non similar triangles which can be formed such that all the angles of the triangles are integers"

My attempt: Let $x$, $y$ and $z$ be the angles of the triangles. So $x+y+z=180$, where $x,y,z \ge1$. Total =$\binom{n-1}{r-1}=\binom{179}{2}=15931$. How to proceed further? We have to subtract the total number of similar triangles from this number.