Answer 1

An n-sided  polygon has n vertices.
By joining any two vertices of the polygon, we obtain either a side or a diagonal of the polygon.
Number of line segments obtained by joining the vertices of an n-sided polygon if we take two vertices at a time = Number of ways of selecting 2 out of n = ⁿC₂
Out of these lines, n lines are sides of the polygon.
Number of diagonals of the polygon = \[{}^n C_2 - n = \frac{n (n - 1)}{2} - n = \frac{n(n - 3)}{2}\]