Question

Polygon has 90 diagonals. how many triangles can be formed through the vertices of the polygon?

Answer 1

no. of triangles will be 91

Answer 2

Answer:

455  triangles can be formed through the vertices of the triangle.

Step-by-step explanation:

Step 1:

Given Data   polygon = 90 diagonals.  

To calculate the number of triangles of the polygon.

Step 2:

Let us assume n be the number of triangle  

Step 3:

Using the Formula:

$\bold{N_{d}=\frac{n(n-3)}{2}}$

Step 4:

n x (n - 3)/2 = 90

n x (n - 3) = 180

$n^{2}$-3 n-180=0

(n-15)(n+12)=0

n=15,-12 (neglect negative value)

n=15

Step 5:

15C3=15!/3!(15-3)!=15!/3!12!

      =15x14x13x12/3x2x1x12

      =5x7x13

      =455