Exterior Angle Calculator

Exterior angles of a polygon are crucial for understanding geometric properties and for solving various mathematical problems. They are particularly important in polygonal shapes where the exterior angle is defined as the angle formed by one side of the polygon and the extension of an adjacent side.

Historical Background

The concept of exterior angles plays a significant role in Euclidean geometry, where it is used to explore the properties of polygons and to prove various theorems.

Calculation Formula

The exterior angle of a polygon can be calculated using the simple formula:

\[ A = \frac{360}{N} \]

where:

• \(A\) is the exterior angle in degrees,
• \(N\) is the number of sides of the polygon.

Example Calculation

For a hexagon, which has six sides:

\[ A = \frac{360}{6} = 60 \text{ degrees} \]

Importance and Usage Scenarios

The concept of exterior angles is essential in determining the shapes of polygons and has applications in various fields, including architecture, engineering, and computer graphics. It's also pivotal in the study of tessellations and patterns.

Common FAQs

1. What is an exterior angle?

   • An exterior angle is the angle formed between a side of a polygon and the extension of its adjacent side.

2. How do you find the exterior angle of a polygon?

   • To find the exterior angle of a polygon, divide 360 degrees by the number of sides of the polygon.

3. Can the exterior angle of a polygon be more than 180 degrees?

   • No, the exterior angle of a polygon is always less than 180 degrees because it is the supplement of the interior angle, which is always less than 180 degrees.

Understanding the properties of exterior angles can help solve complex geometrical problems and is fundamental to the study of polygons.