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South African Mathematics Olympiad

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 $360°$ . There are $180$ exterior angles, which are all equal since the polygon is regular. Thus each exterior angle is equal to $360°/180 = 2°$ , and each interior angle is equal to $180° - 2° = 178°$ .

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