Question

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

Answer 1

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

Explanation:

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