How many sides does a polygon have if the sum of the measures of its interior angles is 1,080

180(n-2) = 1080

180n - 360 = 1080

180n = 1080 + 360

180n = 1440

n = 1440/180

n = 8

The answer is 8 sides.

The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.

Formula for sum of interior angles of a convex polygon is (n - 2)×180°

Let's set the formula equal to our given polygon sum... n = number of sides
(n - 2)×180 = 1080
n - 2 = 6
n = 8

The polygon has 8 sides...octagon