The American. Math 55 is advertised in the Harvard catalog as âprobably the most difficult undergraduate math class in the country.â It is legendary among high school math prodigies, who hear terrifying stories about it in their computer camps and at the Math Olympiads.
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.
That means each of the other angles in the triangle are 70 deg. Since the corner of the nonagon is the sum of the angles of the two triangles that make up the corner, the interior angle of a nonagon is 140 deg. Therefore the exterior angle of a nonagon is (180 - 140) = 40 deg. Each interior angle of a regular nonagon is 140 degrees.