How many diagonals can be drawn by joining the vertices of an octagon?

To solve this elegantly, I will use the 'Handshake' or 'Selection' logic discussed in PYQ 2015 and 2017 [22] [38].\n\n1. **Identify N:** An octagon has 8 vertices (points), so $n = 8$.\n\n2. **Calculate Total Connections:** \n If we connect every point to every other point, it is exactly like the 'Handshake problem' (how many handshakes if 8 people meet). We need to select 2 points out of 8.\n Formula: $8C2$.\n From my PYQ study [41], I have memorized that $8C2 = 28$. \n (Or calculated as $\\frac{8 \\times 7}{2} = 28$).\n\n3. **Isolate Diagonals:**\n These 28 lines include *all* connections. However, 8 of these connections are the outer boundaries (the sides of the octagon) which are not diagonals.\n \n4. **Final Calculation:**\n Diagonals = Total Connections - Sides\n Diagonals = $28 - 8 = 20$.\n\nChecking the options, (A) is 20.