AFOQT Practice Test

The Polygon Angle Sum Theorem states that the sum of the measures of the angles of an n-gon is?

1. (n-2)180

2. n²

3. (n+2)180

4. n x 90

The correct answer is: (n-2)180

The Polygon Angle Sum Theorem indicates that for any polygon with "n" sides, the sum of the interior angles can be calculated using the formula (n-2) × 180 degrees. This formula is derived from the fact that any polygon can be divided into triangles, and since each triangle has an angle sum of 180 degrees, you can determine the angle sum for the polygon by calculating how many triangles can be formed within it. As you can see, if you take a polygon and subtract two from its number of sides, that gives you the number of triangles that can be formed. Multiplying that number by 180 gives you the total measure of all interior angles of the polygon, making this formula the correct representation of the Polygon Angle Sum Theorem. The other options provided do not correctly represent the relationship between the number of sides and the sum of the interior angles of a polygon. For example, squaring the number of sides or adding two, as seen in other choices, does not relate to the properties of polygon angles in a meaningful way.