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

Correct Option

The number of diagonals in any polygon with 'n' vertices (or sides) is calculated using the formula: $\frac{n(n-3)}{2}$.

For an octagon, the number of sides (n) is 8.

Substituting n = 8 into the formula yields:

$\frac{8(8-3)}{2}=\frac{8\times 5}{2}=\frac{40}{2}=20$

Therefore, an octagon has 20 diagonals.

Incorrect Options

Options 2 (24), 3 (28), and 4 (64) are incorrect. These values do not correspond to the number of diagonals in an octagon as determined by the standard geometric formula $\frac{n(n-3)}{2}$.