Question

if a polygon of sides has 1/2n(n-3) diagonals.how many sides will a polygon having 65 diagonals?is there a polygon with 50 diagonals​

Answer 1

Step-by-step explanation:

The number of diagonals of a polygon is given by n(n-3)/2.

So if there are 65 diagonals then the number of sides of the polygon are

65*2 = 130 = n(n-3), or

n^2–3n-130 = 0, or

(n-13)(n+10) = 0, or

n = 13, -10 is not permissible.

Hence the polygon has 13 sides.

Again if the number of diagonals is

50 =n(n-3)/2, or

100 = n^2 - 3n, or

n^2–3n-100 = 0

It has no integral roots, so there is no polygon with 50 diagonals