The problem is:The solution says that the answer is 3+8=11. However, the answer should actually be 3, because if n=8 then the polygon would not be convex.

A convex polygon with nn sides has interior angles of

30∘,60∘,90∘,…,n⋅30∘.30∘,60∘,90∘,…,n⋅30∘.

What is the sum of all possible nn?