Answer:
40 sides
Step-by-step explanation:
The number os sides can be calculated using
[tex]\frac{n(n-3)}{2}[/tex] = d ( n is number of sides and d number of diagonals )
Here d = 740 , then
[tex]\frac{n(n-3)}{2}[/tex] = 740 ( multiply both sides by 2 )
n(n - 3) = 1480
n² - 3n = 1480 ( subtract 1480 from both sides )
n² - 3n - 1480 = 0 ← in standard form
(n - 40)(n + 37) = 0 ← in factored form
Equate each factor to zero and solve for n
n - 40 = 0 ⇒ n = 40
n + 37 = 0 ⇒ n = - 37
A polygon cannot have a negative number of sides.
Then number of sides is 40
