What type of polygon has a sum of its interior angles equal to 1080 degrees?

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To determine the type of polygon that has a sum of its interior angles equal to 1080 degrees, we can use the polygon interior angle sum formula. This formula states that the sum of the interior angles of a polygon with n sides is given by:

Sum = (n - 2) * 180

Where n is the number of sides in the polygon. To find n, we can set the sum equal to 1080 degrees:

(n - 2) * 180 = 1080

Now, we can solve for n:

  1. Divide both sides by 180: 
    n - 2 = 1080 / 180
  2. This simplifies to: 
    n - 2 = 6
  3. Now, add 2 to both sides: 
    n = 6 + 2 = 8

Thus, n is equal to 8, which means that the polygon we are looking for is an octagon. An octagon is a polygon with 8 sides. Therefore, the sum of the measures of the interior angles of an octagon is indeed 1080 degrees.

In summary, if you come across a polygon where the sum of the interior angles is 1080 degrees, you can confidently identify it as an octagon.

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