The polygon that has an interior angle sum of 1080 degrees is a decagon, which is a ten-sided polygon.
To understand why, we can use the formula for finding the sum of the interior angles of a polygon, which is:
Sum of interior angles = (n – 2) × 180
In this formula, n represents the number of sides of the polygon. For a decagon, we have:
- n = 10
- Sum of interior angles = (10 – 2) × 180 = 8 × 180 = 1440 degrees
However, you mentioned a sum of 1080 degrees. This means you are looking for a polygon with 1080 as its interior angle sum, which leads us to solve for n in the formula:
Set up the equation:
1080 = (n – 2) × 180
Now let’s calculate:
- 1080 = 180n – 360
- 180n = 1080 + 360
- 180n = 1440
- n = 1440 / 180
- n = 8
So, the polygon with an interior angle sum of 1080 degrees is an octagon, which has 8 sides.