Question

The number of diagonals in an octagon will be$?$

• A. $28$
• B. $20$
• C. $10$
• D. $16$

Answer 1

The correct option is B

$20$

Explanation for the correct option:

Find the required number of diagonals.

We know that the total number of lines formed through $n$ vertices is given by ${}^{n}C_2$.

Therefore, the total number of lines formed by vertices of an octagon is ${}^{8}C_2=28$.

Since in an octagon there are $8$ sides.

So, the number of diagonals is given by $28-8=20$.

Therefore, the number of diagonals in an octagon is $20$.

Hence, option $B$ is the correct answer.