Polygons and Interior Angles
Polygons and Interior Angles The sum of the interior angles of a polygon follows a specific pattern that depends on n, the number of sides that the polygon has.This sum is always 180° times 2 less than n (the number of sides). i.e (n - 2) x 180 = Sum of Interior Angles of a Polygon Quadrilateral has four sides, the sum of its interior angles is (4 - 2)180 = 2(180) = 360°. Alternatively, note that a quadrilateral can be cut into two triangles by a lineconnecting opposite corners.Thus, the sum of the interior angles of Quadrilateral = 2(180) = 360°. Hexagon has six sides, the sum of its interior angles is (6 - 2)180 = 4(180) = 720°.Alternatively, note that a hexagon can be cut into four triangles by three lines connecting corners.Thus,the sum of the interior angles of Hexagon = 4(180) = 720°.