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Last updated on August 5th, 2025

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Math Formula for the Exterior Angle of a Polygon

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In geometry, the exterior angle of a polygon plays a crucial role in understanding the structure of polygons. The exterior angle is formed by one side of the polygon and the extension of an adjacent side. In this topic, we will learn the formula for calculating the exterior angle of regular polygons.

Math Formula for the Exterior Angle of a Polygon for Canadian Students
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List of Math Formulas for Exterior Angle of a Polygon

Understanding the exterior angle of a polygon is essential in geometry. Let’s learn the formula to calculate the exterior angle for regular polygons.

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Math Formula for Exterior Angle

The exterior angle of a regular polygon is calculated using the formula:

 

Exterior angle formula for a regular polygon = 360°/n where n is the number of sides of the polygon.

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Importance of Exterior Angle Formula

In geometry, understanding the exterior angle formula is crucial for analyzing polygons. Here are some important points about the exterior angle:

 

- The sum of all exterior angles of a polygon is always 360°, regardless of the number of sides.

 

- The exterior angle formula helps in calculating the number of sides of a polygon when the exterior angle is known.

 

- It is used in various geometric constructions and proofs.

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Tips and Tricks to Memorize the Exterior Angle Formula

Some students find geometric formulas tricky and confusing. Here are some tips and tricks to master the exterior angle formula:

 

- Remember that the sum of all exterior angles of any polygon is 360°.

 

- Use the formula 360°/n to calculate the exterior angle of a regular polygon.

 

- Practice with different polygons like triangles, squares, and hexagons to solidify your understanding.

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Real-Life Applications of the Exterior Angle Formula

The concept of exterior angles is used in various real-life applications, such as:

 

- Designing architectural structures that involve polygonal shapes.

 

- Creating tessellations, where the exterior angle plays a role in the pattern formation.

 

- Solving problems in navigation and geography where polygons are involved.

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Common Mistakes and How to Avoid Them While Using the Exterior Angle Formula

Students often make errors when calculating exterior angles. Here are some mistakes and ways to avoid them to master the concept.

Mistake 1

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Confusing interior and exterior angles

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Students sometimes mix up interior and exterior angles. To avoid this, remember that the exterior angle is formed by one side of the polygon and the extension of its adjacent side.

Mistake 2

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Using the wrong formula for irregular polygons

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The formula 360°/n is only applicable to regular polygons. For irregular polygons, students should calculate each exterior angle individually.

Mistake 3

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Incorrectly identifying the number of sides

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Students might miscount the number of sides of the polygon, leading to incorrect results. Double-check the number of sides before using the formula.

Mistake 4

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Forgetting the sum of exterior angles

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Students may forget that the sum of all exterior angles in any polygon is 360°. Keep this in mind to avoid errors in calculations.

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Examples of Problems Using the Exterior Angle Formula

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Problem 1

What is the exterior angle of a regular pentagon?

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The exterior angle is 72°

Explanation

A regular pentagon has 5 sides. Using the formula 360°/n, we have: Exterior angle = 360°/5 = 72°

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Problem 2

Find the exterior angle of a regular octagon.

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The exterior angle is 45°

Explanation

A regular octagon has 8 sides. Using the formula 360°/n, we have: Exterior angle = 360°/8 = 45°

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Problem 3

Calculate the exterior angle of a regular hexagon.

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The exterior angle is 60°

Explanation

A regular hexagon has 6 sides. Using the formula 360°/n, we have: Exterior angle = 360°/6 = 60°

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FAQs on Exterior Angle Formula

1.What is the exterior angle formula for a polygon?

The exterior angle formula for a regular polygon is: Exterior angle = 360°/n, where n is the number of sides of the polygon.

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2.Why is the sum of the exterior angles of any polygon 360°?

The sum of the exterior angles of any polygon is 360° because each exterior angle represents a full turn around the polygon.

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3.How do I find the number of sides of a polygon if the exterior angle is given?

To find the number of sides of a polygon when the exterior angle is given, use the formula: n = 360°/Exterior angle.

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Glossary for Exterior Angle Formula

  • Exterior Angle: The angle formed by one side of a polygon and the extension of an adjacent side.

     
  • Regular Polygon: A polygon with all sides and angles equal

     
  • Interior Angle: The angle formed inside a polygon by two adjacent sides.

     
  • Polygon: A closed figure with at least three straight sides and angles.

     
  • Angle Sum Property: The sum of the exterior angles of any polygon is always 360°.
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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