How to find each exterior angle of a polygon: A simple guide to understanding exterior angles in polygons

To find each exterior angle of a regular polygon, you simply need to divide 360 degrees by the number of sides the polygon has. This is because the sum of all exterior angles in any polygon is always 360 degrees, regardless of the number of sides. For example, if you’re working with a regular hexagon (6 sides), each exterior angle would be 360° ÷ 6 = 60°. This formula works only for regular polygons, where all sides and angles are equal. For irregular polygons, the exterior angles can be different, but their sum still adds up to 360 degrees.

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As a designer, I view geometry as a foundational design language. Accurately calculating exterior angles can help ensure precise joinery in structures, symmetrical façade layouts, or even furniture design elements that rely on polygonal shapes. For beautifully visualizing how polygons will fit and flow in a room or on a façade, leveraging a floor planning tool can make these calculations both intuitive and immediately actionable during your design process.

FAQ

Q: What is the formula for each exterior angle of a regular polygon?

A: The formula is 360° divided by the number of sides (n): Each angle = 360° / n.

Q: Do all exterior angles of a regular polygon have the same value?

A: Yes, in a regular polygon all exterior angles are equal.

Q: What if the polygon is irregular?

A: The exterior angles will vary, but their sum will always be 360 degrees.

Q: Why do the exterior angles of any polygon always sum to 360 degrees?

A: This is a geometric property: as you "walk" around the polygon, making one turn at each vertex, you complete a full circle (360°).

Q: How can I use exterior angles in design planning?

A: Understanding these angles supports accurate patterning, layout design, and ensuring symmetrical repetition—vital for tile, panel, and fixture placements in interiors.