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

Question

The number of diagonals that can be drawn by joining the vertices of an octagon, is (A)  28  (B)  48  (C)  20  (D)  15

Tardigrade Admin · Accepted Answer

By joining any two points of a vertices, we get a diagonal, but we have to subtract the sides of a octagon. ∴ Number of diagonals =8C2-8 =(8× 7/2× 1)-8=20

Q. The number of diagonals that can be drawn by joining the vertices of an octagon, is

$28$

$48$

$20$

$15$

By joining any two points of a vertices, we get a diagonal, but we have to subtract the sides of a octagon.
$∴$ Number of diagonals $=^{8} C_{2} - 8$
$= \frac{8 \times 7}{2 \times 1} - 8 = 20$