By using the polygon diagonal formula or the quadratic equation formula in which in both formulae they work out that the polygon in question has 21 sides.
It is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
number of diagonals = n(n-3)/2 n - number of sides of the polygon
1/2*(n2-3n) = 665 diagonals where n means number of sides
Using the formula (x)(x-3)/2 = Diagonals ; simply replace the diagonals with the number of diagonals you're given. Then, you'll havev (x)(x-3)/2 = Diagonals. Simplify it, and you'll be given x(power of 2) - 3X = (2)(Diagonals). Subtract the amount of diagonals from both sides, and you'll have x(power of 2) - 3X - 2Diagonals = 0. From there, use the quadratic formula to find the number of sides the polygon has.
A polygon with n sides has n*(n - 3)/2 diagonals. So n = 23 gives 23*20/10 = 230 diagonals
A 7 sided polygon has 14 diagonals
The five sided Polygon has 5 diagonals
The rule is: 0.5*(N2-3N) = number of diagonals
Number of diagonals = 1/2*(n2-3n) where n = the number of sides of the polygon.
38 diagonals
It has 20 diagonals
It is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
The formula is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon
A polygon with 14 diagonals will have 7 sides
11
209
The equation is: 0.5*(n2-3n) = diagonals whereas n is the number of sides of the polygon