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