Calculating Degrees of An Exterior Angle of A Circle

An exterior angle of a circle is an angle formed by one side of a polygon and the extension of an adjacent side. Calculating its degrees is essential in geometry, engineering, and architecture. This guide explains the formula, provides a calculator, and includes practical examples.

What is an Exterior Angle of a Circle?

An exterior angle of a circle is formed when you extend one side of a polygon and measure the angle between this extension and the adjacent side. For a regular polygon (where all sides and angles are equal), the exterior angle can be calculated using a simple formula.

Exterior angles are important in various fields:

Geometry: Understanding angle relationships in polygons
Engineering: Designing structures with precise angular measurements
Architecture: Creating accurate building plans
Computer Graphics: Rendering 3D models with proper angular relationships

How to Calculate Exterior Angle Degrees

Calculating the degrees of an exterior angle of a circle involves these steps:

Identify the number of sides in the polygon
Use the formula for exterior angle calculation
Apply the formula to get the angle in degrees

The calculation is straightforward once you know the number of sides. For irregular polygons, you may need to measure each exterior angle individually.

The Formula

The formula to calculate the degrees of an exterior angle of a regular polygon is:

Exterior Angle = 360° / Number of Sides

This formula works because the sum of all exterior angles of any polygon is always 360 degrees. By dividing this total by the number of sides, you get the measure of each exterior angle.

Worked Example

Let's calculate the exterior angle of a regular hexagon (6 sides):

Number of sides = 6
Exterior Angle = 360° / 6 = 60°

So, each exterior angle of a regular hexagon measures 60 degrees.

For irregular polygons, you would need to measure each exterior angle individually using a protractor or angle measuring tool.

FAQ

What is the difference between interior and exterior angles?: Interior angles are the angles inside the polygon at each vertex, while exterior angles are formed by extending one side and measuring the angle between this extension and the adjacent side.
Can exterior angles be greater than 180 degrees?: Yes, for concave polygons, exterior angles can be greater than 180 degrees. The sum of exterior angles for any polygon is always 360 degrees.
How do I measure an exterior angle?: To measure an exterior angle, extend one side of the polygon and use a protractor to measure the angle between this extension and the adjacent side.
What's the relationship between exterior angles and central angles?: In a regular polygon, each central angle (angle from the center to two adjacent vertices) is equal to the exterior angle. For irregular polygons, this relationship doesn't hold.
Can I calculate exterior angles for non-polygon shapes?: The concept of exterior angles is specifically defined for polygons. For other shapes, you would need to define what constitutes an "exterior angle" for that specific shape.