Question:

<p><strong>Step 1:</strong> The total number of line segments joining <i>n</i> vertices is:</p><p>$$\binom{n}{2} = \frac{n(n-1)}{2}$$</p><p><strong>Step 2:</strong> Out of these, <i>n</i> are the sides of the polygon.</p><p><strong>Step 3:</strong> Therefore, the number of diagonals is:</p><p>$$\binom{n}{2} - n = \frac{n(n-1)}{2} - n = \frac{n(n-1) - 2n}{2} = \frac{n(n-3)}{2}$$</p>