AFOQT Practice Test

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How are the interior angles of a polygon calculated?

Sum of interior angles = n x 180
Sum of interior angles = (n-2) x 90
Sum of interior angles = (n-2) x 180
Sum of interior angles = n x 360

The correct answer is: Sum of interior angles = (n-2) x 180

The formula for calculating the sum of the interior angles of a polygon is indeed based on the number of sides, denoted as 'n'. The correct formulation is that the sum of the interior angles can be determined using the formula (n - 2) x 180. This is derived from the fact that any polygon can be divided into triangles. For every polygon with 'n' sides, you can draw diagonals from one vertex to create 'n - 2' triangles. Since the sum of the angles in each triangle is 180 degrees, multiplying the number of triangles by 180 gives you the total sum of the interior angles for the polygon. Thus, using this formula allows you to accurately calculate the interior angles for polygons with any number of sides beyond three, which is where the concept of triangulation becomes applicable.