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.
Since the measure of an exterior angle equals the sum of its two non-adjacent interior angles, the exterior angle is also greater than either of the individual non-adjacent interior angles. and also. Theorem: The measure of an exterior angle of a triangle is greater than either of its two non-adjacent interior angles.t is always helpful to draw a diagram and label it with the given information. Then, using the first theorem above, set the exterior angle (x) equal to the sum of the two non-adjacent interior angles which are 45Â° and 72Â°. x = 45 + 72 x = 117. So, an exterior angle at P measures 117Â°.