What is the sum of the measures of the interior angles of the regular polygon shown above?
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The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent.
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. The sum S of the interior angle measures of a polygon with n sides is S = (n − 2) ⋅180°.
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