What is the sum of the interior angles of a polygon that has a total of 3740 diagonals?

1 Answer
Jun 11, 2018

15480°

Explanation:

I guess I will just answer my own question after two months.

The equation for diagonals:

D=(n(n-3))/2
n= number of sides the polgyon has

Now let’s plug in 3740 as D in the equation.

3740=(n(n-3))/2

To cancel the denominator 2 out, multiply both sides by 2:

7480= n^2 -3n

Let’s have both the variables and the constant on one side set to =0. To do this, you subtract 7480 from both sides.

n^2 -3n -7480 =0

Factor the equation out:

(n+85)(n-88)

Set n+85=0 and n-88=0

n=-85 or n=88

We cannot use n=-85 in our search for the sum of interior angles because a polygon cannot have negative sides. So let’s use
n=88.

This is the equation to find the sum of interior angles:

180(n-2)

Now that we have the number of sides of the polygon, we can plug it into the equation:

180(88-2)

15480°

Hope this helps someone out!