Angles of a regular polygon

You have already seen that the sum of the exterior angles is 360^\circ and that the interior and the exterior angles add up to 180^\circ. A regular polygon is a polygon whose interior angles are all equal. Use this information to find the exterior and interior angles of a regular polygon.


Find the exterior and interior angle of a regular pentagon.

A pentagon has {5} sides and {5} exterior angles. The exterior angles add up to 360^\circ.

one~exterior~angle = 360^\circ \div 5 = 72^\circ

interior~angle = 180  - exterior~angle = 180 - 72 = 108^\circ

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