Is it possible for a regular polygon to have an interior angle measure of 130°? Explain.

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Answer 1 · 2017-12-31T21:03:18

$130°$ is not possible for the interior angles of a regular polygon

If the interior angle is $130°$ then the exterior angle will be $50°$

The sum of the exterior angles is always $360°$ and we can use this fact to find the number of sides.

$360° div 50° = 7.2 " sides"$

The number of sides has to be a natural number, so $7.2$ is not possible, therefore $130°$ is not possible for the angles of a regular polygon.

Also consider the interior angles of regular polygons.

Pentagon: $540/5 = 108°$

Hexagon: $720/6 = 120°$

Heptagon: $900/7 = 128.57°$

Octagon: $1080/8 = 135°$

There is no polygon between one with 7 sides and one with 8 sides.

$130°$ is not possible