Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What formula is used to calculate the sum of the interior angles of a polygon?

(n-2)180
(n+2)180
(n-3)180
(n+3)180

The correct answer is: (n-2)180

To calculate the sum of the interior angles of a polygon, the formula used is (n-2)180, where n represents the number of sides in the polygon. This formula derives from the fact that any polygon can be divided into triangles, and each triangle has a sum of interior angles equal to 180 degrees. For instance, if you have a triangle (3 sides), you can see that (3-2)180 = 1 * 180 = 180 degrees, which is correct. For a quadrilateral (4 sides), (4-2)180 = 2 * 180 = 360 degrees, which is also correct because it consists of two triangles. Similarly, for any polygon with more than four sides, the formula accounts for the fact that as you add sides, you can always form two additional triangles per new side added beyond the third side. The other options presented do not accurately reflect the relationship between the number of sides and the total sum of angles in a polygon. Therefore, (n-2)180 is the correct choice for computing the sum of the interior angles of any polygon.