Find the measure of one interior angle of a regular hexagon

Find the measure of one interior angle of a regular hexagon. _____ The measure of an exterior angle of a regular n-gon is 72 degree. Classify the polygon by number of sides. ______ Solve for x. x = ____ The measure of an interior angle of a regular n-gon is 140 degree. How many sides are in the regular polygon? _____

Solution

A regular hexagon has 6 sides of equal length and all internal angles of a regular hexagon are equal. The sum of internal angles of a hexagon is given by (n-2)×180 where n is the total number of sides since hexagon has total six sides and sum of internal angles is (6-2)×180=720 degree and as all internal angles of a regular hexagon is equal therefore each internal angle will be 720/6=120 degree.

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