Answer :
Let n be the number of vertices of the polygon.
then there are n sides.
N = number of all connections between all the vertices =
[tex]{}^nC_2[/tex]
N = n(n-1)/2
Number of diagonals = N - n = n (n - 3)/2 = 27 given
n² - 3 n - 54 = 0
(n - 9) (n + 6) = 0
n = 9
so there are 9 sides and 9 vertices
then there are n sides.
N = number of all connections between all the vertices =
[tex]{}^nC_2[/tex]
N = n(n-1)/2
Number of diagonals = N - n = n (n - 3)/2 = 27 given
n² - 3 n - 54 = 0
(n - 9) (n + 6) = 0
n = 9
so there are 9 sides and 9 vertices
Answer:
9
Step-by-step explanation:
n(n-3)/2 = 27
n(n-3) = 54
n2 - 3n = 54
n2-9n+6n = 54
n(n-9)+6(n-9)=54
n = -6 or 9
excluding the negative
n = 9
ans...//