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.
An octagon is an 8 sided polygon with interior angles that add to 1080 degrees. Regular octagons have sides of equal length and interior angles of 135 degrees. A nonagon is a 9 sided polygon with interior angles that add to 1260 degrees.Regular nonagons have sides of equal length and interior angles of 140 degrees. square is a 4 sided polygon with interior angles that add to 360 degrees. A square is also a type of quadrilateral. A pentagon is a 5 sided polygon with interior angles that add to 540 degrees. Regular pentagons have sides of equal length and interior angles of 108 degrees.