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.
We know that a straight line always measures 180 degrees. So because your interior and exterior angles together make up a straight line, they are supplementary. You know how to find the measure of your interior angle, so your exterior angle is simply 180 - Interior Angle. For the triangle, 180 - 60 = 120. 120 degrees is the measure of the exterior angle.