How many sides does a polygon have if the sum of its angle measures is 2880 degrees?

To find the number of sides (n) in a polygon when given the sum of its angle measures, we can use the following formula:

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

In this case, we’re told that the sum of the angle measures is 2880 degrees. So we can set up the equation:

(n – 2) × 180 = 2880

Now, let’s solve for (n):

1. First, divide both sides of the equation by 180:

(n - 2) = 2880 / 180

2. Calculating the right side gives:

(n - 2) = 16

3. Next, add 2 to both sides:

n = 16 + 2

4. This simplifies to:

n = 18

Thus, a polygon with a sum of interior angles equal to 2880 degrees has 18 sides.