A figure of | 3 sides is | called a | Trigon. |
" | 4
| " | Tetragon. |
polygon | 5 | " | Pentagon. |
" | 6 | " | Hexagon. |
" | 7 | " | Heptaagon. |
" | 8 | " | Octagon. |
" | 9 | " | Enneagon or Nonagon. |
The angles of regular polygons are designated by their degrees of angle, "at the centre" and "at the circumference." By the angle at the centre is meant the angle of a side to a radial line; thus in Figure 73 is a hexagon, and at C is a radial line; thus the angle of the side D to C is 60 degrees. Or if at the two ends of a side, as A, two radial lines be drawn, as B, C, then the angles of these two lines, one to the other, will be the "angle at the centre." The angle at the circumference is the angle of one side to its next neighbor; thus the angle at the circumference in a hexagon is 120 degrees, as shown in the figure for the sides E, F. It is obvious that as all the sides are of equal length, they are all at the same angle both to the centre and to one another. In Figure 74 is a trigon, the angles at its centre being 120, and the angle at the circumference being 60, as marked.
The angles of regular polygons:
Trigon, at | the centre, | 120°, | at the | circumference, | 60°. |
Tetragon, | " | 90°, | " | " | 90°. |
Pentagon, | " | 72°, | " | " | 108°. |
Hexagon, | " | 60°, | " | " | 120°. |
Octagon, | " | 45°, | " | " | 135°. |
Enneagon, | " | 40°, | " | " | 140°. |
Decagon, | " | 36°, | " | " | 144°. |
Dodecagon, | " | 30°, | " | " | 150°. |