Question

The number of diagonals that can be drawn by joining the vertices of an octagon is:

• A. 28
• B. 24
• C. 20
• D. 26

Hint:

Use the diagonal formula \( \frac{n(n - 3)}{2} \) to calculate the number of diagonals in any polygon with \( n \) sides.

Answer 1

The Correct Option is C

The formula to calculate the number of diagonals in a polygon with \( n \) sides is: \[ \text{Number of diagonals} = \frac{n(n - 3)}{2} \] 
Step 1: In an octagon, \( n = 8 \). 
Step 2: Apply the formula: \[ \text{Number of diagonals} = \frac{8(8 - 3)}{2} = \frac{8 \times 5}{2} = \frac{40}{2} = 20 \] Thus, the number of diagonals in an octagon is 20.