Exterior Angle of a Polygon Calculator


Exterior Angle of a Polygon Calculator

Greetings, polygon ponderers! Remember that time in school when polygons seemed like just a bunch of lines? Well, buckle up because we are about to embark on a thrilling journey into the realm of exterior angles of polygons! (Okay, we get it, not everyone’s idea of a rollercoaster ride, but bear with us, it’s less hair-raising than you might think!)


No witchcraft here, the formula for calculating the exterior angle of a polygon is as simple as pie (not the eatable one):

360 / Number of sides

Categories of Exterior Angles

Here’s a cheat sheet for you, a table outlining different categories of exterior angles. Remember, the more sides, the less angle (don’t tell the circle, it’s sensitive about having no sides):

Category Angle Range
Triangle 120 degrees
Square 90 degrees
Pentagon 72 degrees
Hexagon 60 degrees
Heptagon 51.43 degrees
Octagon 45 degrees


Ever wanted to know how a triangle feels when it realizes it has the largest exterior angle? Or why the octagon is always so right (angle)? Here are some examples:

Polygon Number of sides Exterior Angle Calculation
Triangle 3 120 degrees 360/3
Square 4 90 degrees 360/4
Pentagon 5 72 degrees 360/5

Calculation Methods

As with any quest, there are several paths you can take. Here are the most popular ways to calculate exterior angles, each with its own perks and pitfalls:

Method Advantages Disadvantages Accuracy
Manual Calculation Simple, no tools needed Prone to human error High if done correctly
Calculator High accuracy, quick Requires a calculator Very high

Evolution of the Concept

The concept of exterior angles has evolved over time, just like our understanding of why pizza tastes so good. Here’s a brief history lesson:

Time Period Changes in Concept
Ancient Times Basic understanding of angles and shapes
Middle Ages Further development in geometry
Modern Times Advanced calculators and software

Limitations of Accuracy

While we strive for perfection, there are some limitations to be aware of when calculating exterior angles:

  1. Human Error: Even the best of us can make mistakes when calculating manually.
  2. Complex Polygons: The more sides a polygon has, the more room for error in the calculation.

Alternative Methods

Sometimes the path less traveled offers a fresh perspective. Here are some alternative methods for calculating exterior angles:

Method Pros Cons
Using a protractor Simple, visual Less accurate
Using software Quick, accurate Requires access to the software


  1. What is an exterior angle? It’s the angle formed between any side of a shape and a line extended from the next side.
  2. How do you calculate the exterior angle of a polygon? Easy peasy! Just divide 360 by the number of sides.
  3. What is the exterior angle of a square? A square has an exterior angle of 90 degrees.
  4. Why is the exterior angle sum always 360? No matter how many sides a polygon has, if you add up all the exterior angles, the total is always 360 degrees.
  5. Can a polygon have an exterior angle greater than 180 degrees? Nope, exterior angles are always less than or equal to 180 degrees.
  6. What’s the difference between interior and exterior angles? Interior angles are inside the polygon, while exterior angles are outside, formed by extending one of the sides.
  7. How does the number of sides affect the exterior angle? The more sides a polygon has, the smaller each exterior angle will be.
  8. What is the exterior angle of a regular polygon? For a regular polygon (where all sides and angles are equal), the exterior angle is 360 divided by the number of sides.
  9. Can I calculate the exterior angle without knowing the number of sides? Unfortunately, no. The number of sides is crucial in calculating the exterior angle.
  10. Why are exterior angles important? They are fundamental in geometry and used in many fields, from architecture to graphic design.


  1. US Department of Education: Provides educational resources and research materials. Link
  2. National Center for Education Statistics: Offers a wide range of statistics and data related to education. Link