The Exterior Angle Calculator is a specialized online tool designed to simplify the process of determining the measure of an exterior angle of any polygon. An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent side. Understanding the measure of exterior angles is crucial in various fields of geometry, architecture, and design.
The primary function of the Exterior Angle Calculator is to provide users with an instant calculation of the exterior angle of a polygon, given the number of sides of the polygon. This not only aids in academic learning but also supports professionals in relevant fields to make accurate measurements and decisions in their work.
Formula
To ensure clarity and utility, the calculator operates on a straightforward mathematical formula:
Exterior Angle = 360 / Number of Sides
Where:
- Exterior Angle is the measure of the angle form outside the polygon.
- Number of Sides is the total number of sides in the polygon.
This formula is derived from the principle that the sum of the exterior angles of any polygon equals 360 degrees, a fundamental concept in geometry.
Table for General Terms
To enhance the utility of this guide. Below is a table of general terms related to the exterior angles of common polygons. Offering a quick reference without the need for calculations:
Polygon Type | Number of Sides | Exterior Angle |
---|---|---|
Triangle | 3 | 120° |
Square | 4 | 90° |
Pentagon | 5 | 72° |
Hexagon | 6 | 60° |
Heptagon | 7 | 51.43° |
Octagon | 8 | 45° |
This table serves as a handy reference for common polygons, providing immediate insights into the measure of their exterior angles.
Example
Let's illustrate the use of the Exterior Angle Calculator with an example. Consider a hexagon, which has six sides. Using the formula provided:
Exterior Angle = 360 / 6 = 60°
This means each exterior angle of a hexagon measures 60 degrees.
Most Common FAQs
An exterior angle of a polygon is form by one side of the polygon and the extension of an adjacent side. It lies outside the polygon.
You can calculate the exterior angle of a polygon by dividing 360 degrees by the number of sides of the polygon. The formula is Exterior Angle = 360 / Number of Sides
.
Yes, the Exterior Angle Calculator is reliable for professional use, provide it is use correctly. It is based on a fundamental geometric principle and delivers accurate measurements.