Final answer:
The sum of the measures of the angles of an n-gon, according to the Polygon Angle-Sum Theorem, is (n - 2) × 180 degrees.
Step-by-step explanation:
The question, "The polygon Angle-Sum theorem states; The sum of the measures of the angles of an n-gon is ___.", pertains to a fundamental concept in geometry. According to the Polygon Angle-Sum Theorem, the sum of the angle measures in an n-gon (a polygon with n sides) is given by the formula (n - 2) × 180 degrees. So, for example, in a triangle (which is a 3-gon), the sum of the angles is (3 - 2) × 180 degrees, which equals 180 degrees.
When dealing with more complex polygons, this formula remains consistently applicable. For instance, a quadrilateral (4-gon) would have an angle sum of (4 - 2) × 180 degrees = 360 degrees, and so on for polygons with more sides.