Question Detail

From an n-sided polygon, we can choose any two vertices to form a line segment. The number of ways to choose 2 vertices from n vertices is nC2 = n(n-1)/2.These line segments include both the sides of the polygon and its diagonals. An n-sided polygon has n sides. Therefore, the number of diagonals = (Total number of line segments between any two vertices) - (Number of sides of the polygon).Number of diagonals = nC2 - n = n(n-1)/2 - n = (n(n-1) - 2n)/2 = (n² - n - 2n)/2 = (n² - 3n)/2 = n(n-3)/2.