To determine what polygon has an interior angle sum of 1080 degrees, we can use the formula for the sum of the interior angles of a polygon, which is:
Sum = (n – 2) × 180
Here, n represents the number of sides of the polygon. We need to find the value of n for which the sum equals 1080 degrees.
We start by setting the equation:
(n – 2) × 180 = 1080
Next, we can simplify the equation:
n – 2 = 1080 / 180
This simplifies to:
n – 2 = 6
Now, we can solve for n:
n = 6 + 2 = 8
This means the polygon has 8 sides, which is known as an octagon. Therefore, a polygon with an interior angle sum of 1080 degrees is an octagon.