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 angle is a measure of rotation. Angles are measured in degrees. One complete rotation is measured as 360Â°. Angle measure can be positive or negative, depending on the direction of rotation. The angle measure is the amount of rotation between the two rays forming the angle. Rotation is measured from the initial side to the terminal side of the angle. Positive angles (Figure a) result from counterclockwise rotation, and negative angles (Figure b) result from clockwise rotation. An angle with its initial side on the xâaxis is said to be in standard position.