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Objective: After studying this section, you will be able to recognize regular polygons and use a formula to find the measure of an exterior angle of an equiangular polygon. Regular polygons: a few examples Equilateral Triangle Regular Pentagon Square Regular Hexagon Notice anything in common between these polygons? A regular polygon is a polygon that is both equilateral and equiangular 1 In the last lesson you learned that the sum of the exterior angles is 360 for any polygon. In a regular polygon all the angles inside are equal so the exterior angles should be equal as well. If we take 360 and divide by 5 (there are 5 angles) we will get the measure of angle 1. 360 m1 72 5 The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula 360 E n How many degrees are there in each exterior angle of an equiangular heptagon? If each exterior angle of a polygon is 18 degrees, how many sides does the polygon have? If each angle of a polygon is 108 degrees, how many sides does the polygon have? Find the measure of each angle of a regular octagon Find the measure of each exterior angle of an equilateral quadrilateral Explain why the statement “If a polygon is equiangular, then it is a regular polygon” is false. Worksheet