Question

The sum of the interior angles of a polygon is 1980°.how many sides has the polygon​

Answer 1

To know how many sides has this polygon, knowing the sum of their interior angles, we can use this expression:

b = (n-2) * 180

Where b is the sum of the interior numbers and n the number of sides.

Knowing this, we can replace, as we kno w it

b = (n-2)) * 180

1980 = (n-2)*180

We can know solve the equation

We can use this distributive property to operate the parenthesis, which says that if we find this expression a(b+c), we can operate doing ab+ac, and, if we substract, we can also use it, as a(b-c) = ab-ac

1980 = (n-2)*180

1980 = 180n - 180*2 = 180n - 360

1980 = 180n - 360

1980 + 360 = 180n

`(1980+360)/(180) = n.`

13 = n

So we know the polygon will have 13 sides..

Answer 2

sum of interior angle of polygon = (2N-4) X 90 where N =number of sides

so (2N-4)x90=1980

therefore N=13.

therefore polygon has 13 sides