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Geometry Difficulty 3.8 AMC 10/12 Find the answer South Africa

Each interior angle of a regular 180 sided polygon is equal to

Pick one

Solution

It is easier to work with exterior angles, since the sum of the exterior angles of a polygon is 360°360°. There are 180180 exterior angles, which are all equal since the polygon is regular. Thus each exterior angle is equal to 360°/180=2°360°/180 = 2°, and each interior angle is equal to 180°2°=178°180° - 2° = 178°.

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