what is always the measure of one interior angle of a regular nonagon
Each interior angles of a regular nonagon measures 140^o Sum of all interior angles of any convex N-sided polygon equals to (N-2)180^o The proof of this is simple. Pick an initial point O inside a polygon, connect it with all vertices, forming N triangles. Sum of all angles of these triangles is N*180^o. To get a sum of all interior angles we should subtract a sum of all angles lying around that initial point O, that is we have to subtract 360^o.