Only 22 Regular Polygons
Have Integer Angles
A regular polygon has all angles and all sides equal.
Rather than using the polygon calculator constantly, this table was created to show the angles for some of the more commonly encountered regular polygons.
There are just 22 regular polygons that have angles which are integers.
Note: the triangle is sometimes (though rarely) referred to as a trigon and
the square is sometimes referred to as a tetragon.
| Polygon NAME | Polygon SIDES | Each Interior ANGLE | Central ANGLE Equals Exterior Angle = | Interior ANGLE Total |
|---|---|---|---|---|
| Triangle (Trigon) | 3 | 60 | 120 | 180 |
| Square (Tetragon) | 4 | 90 | 90 | 360 |
| Pentagon | 5 | 108 | 72 | 540 |
| Hexagon | 6 | 120 | 60 | 720 |
| Octagon | 8 | 135 | 45 | 1,080 |
| Nonagon | 9 | 140 | 40 | 1,260 |
| Decagon | 10 | 144 | 36 | 1,440 |
| Dodecagon | 12 | 150 | 30 | 1,800 |
| Pentadecagon | 15 | 156 | 24 | 2,340 |
| Octadecagon | 18 | 160 | 20 | 2,880 |
| Icosagon | 20 | 162 | 18 | 3,240 |
| Icositetragon | 24 | 165 | 15 | 3,960 |
| Triacontagon | 30 | 168 | 12 | 5,040 |
| Triacontahexagon | 36 | 170 | 10 | 6,120 |
| Tetracontagon | 40 | 171 | 9 | 6,840 |
| Tetracontapentagon | 45 | 172 | 8 | 7,740 |
| Hexacontagon | 60 | 174 | 6 | 10,440 |
| Heptacontadigon | 72 | 175 | 5 | 12,600 |
| Enneacontagon | 90 | 176 | 4 | 15,840 |
| – | 120 | 177 | 3 | 21,240 |
| – | 180 | 178 | 2 | 32,040 |
| – | 360 | 179 | 1 | 64,440 |
