120 Gon Number

Introduction

In geometry, a polygon is a closed plane figure with three or more straight sides. A 120-gon is a polygon with 120 sides. The 120 gon can be both regular and irregular.

In mathematics, there are various properties for polygons and 120-gon is no exception. In this article, we will explore some of these properties and the ways in which we can calculate them mathematically.

Properties of a 120-gon

Interior Angles

The sum of the interior angles of a polygon with n sides (assuming no crossing of lines) is given by the formula:

(sum of interior angles) = (n - 2) * 180 degrees

For a 120-gon, n = 120, therefore:

(sum of interior angles) = (120 - 2) * 180 degrees = 21120 degrees

Exterior Angles

The sum of the exterior angles of a polygon with n sides is always 360 degrees. Therefore, the exterior angle for a regular 120-gon would be:

(exterior angle) = 360 / n = 3 degrees

Diagonals

A diagonal is a line that connects any two non-adjacent vertices in a polygon. The number of diagonals in a polygon can be calculated using the following formula:

(number of diagonals) = n(n-3)/2

For a 120-gon, n = 120, therefore:

(number of diagonals) = 120(120-3)/2 = 7020 diagonals

Conclusion

In this article, we have explored some of the properties of a 120-gon, including its interior and exterior angles, as well as its diagonals. These properties can be calculated using mathematical formulas and can be useful in various applications, such as in the fields of architecture and design.