How many diagonals are there in a polygon with n=50 sides?
In a polygon, the sides are the lines that join consecutive points. All other lines between points that form the polygon are called diagonals.
For example, the simplest polygon which is a triangle does not have any diagonals as all the lines drawn between points that form the polygon are sides of the triangle. A rectangle has 4 sides and 2 diagonals.
The number of sides that a polygon has is equal to the number of points that make up the polygon. As examples, triangles have 3 sides and are formed by 3 points, rectangles have 4 sides and are formed by 4 points, etc.
A polygon with 50 sides is formed by 50 points. The number of lines joining consecutive points is 50 and these are the sides of the polygon. All lines between non-consecutive points are called diagonals.
From each point of the polygon we can draw 47 diagonals. But the diagonal between two points is the same irrespective of which point is considered the starting point and which is considered the ending point. This gives the number of diagonals as 50*47/2 = 1175
The number of diagonals in a polygon with 50 sides is 1175.