Question

if number of diagonals of a polygon is 8 times the number of sides, the number of sides in the polygon is

Answer 1

The number of sides in the polygon is 19.

Step-by-step explanation:

Let's denote the number of sides of the polygon as n. The number of diagonals in any polygon can be found using the formula D = (n(n-3))/2, where D is the number of diagonals. According to the given condition, we have 8n = (n(n-3))/2.

Simplifying this equation, we get 16n = n^2 - 3n.

Rearranging the equation, we have n^2 - 19n = 0.

Factoring out n, we get n(n - 19) = 0.

So, n = 0 or n = 19. Since a polygon cannot have 0 sides, the number of sides in the polygon is 19.

Learn more about Number of sides in a polygon