Graduate Management Admission Test (GMAT) Practice Test

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How do you calculate the sum of interior angles of a polygon with n sides?

(n-2) * 90°
(n-2) * 180°
(n+2) * 180°
n * 180°

The correct answer is: (n-2) * 180°

To calculate the sum of the interior angles of a polygon with n sides, you use the formula (n-2) * 180°. This formula is derived from the fact that any polygon can be divided into (n-2) triangles. Since the sum of the interior angles of a triangle is always 180°, the total sum for a polygon is the number of triangles multiplied by 180°. For example, a triangle (3 sides) has a sum of interior angles equal to (3-2) * 180° = 1 * 180° = 180°. A quadrilateral (4 sides) has (4-2) * 180° = 2 * 180° = 360°, and so on. This clearly illustrates that the formula holds for polygons of varying sides. The other options do not represent the correct relationships for calculating the sum of a polygon's interior angles. Using (n-2) * 90° would not account for the angles in a triangle correctly, as each triangle contributes 180°, not 90°. The formula (n+2) * 180° inaccurately adds extra angles that are not part of the polygon's configuration. Lastly, n * 180° would imply