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Each exterior angle of a regular polygon is 30degree.Find the sum of the intesior angles of the polygon

sum of the exterior angles is 360

360 / 30 = 12 sides ... and interior angles

sum = (180 - 30) * 12

Did you know?

Did you know that the sum of the interior angles of a polygon can be found using a simple formula? In the case of a regular polygon, where all sides and angles are equal, each exterior angle can be calculated as 360 degrees divided by the number of sides. In this particular example, where each exterior angle is 30 degrees, we can determine that the number of sides in the polygon is 360 degrees divided by 30 degrees, which equals 12 sides. With this information, we can now use the formula for the sum of interior angles in a polygon: (number of sides - 2) multiplied by 180 degrees. Substituting the value of 12 for the number of sides, we find that the sum of the interior angles of this regular polygon is 10 multiplied by 180 degrees, which equals 1800 degrees.