The sum of the angle measures of a polygon with n sides is 2880, find n

To find the number of sides (n) in a polygon where the sum of the interior angle measures is 2880 degrees, we can use the formula for the sum of the interior angles of a polygon:

Sum of interior angles = (n – 2) × 180

Here, n represents the number of sides in the polygon. We need to set up an equation using this formula:

(n – 2) × 180 = 2880

Now, let’s solve for n:

1. First, divide both sides of the equation by 180:
2. (n – 2) = 2880 / 180
3. (n – 2) = 16
4. Now, add 2 to both sides:
5. n = 16 + 2
6. n = 18

So, the polygon has 18 sides.