Detailed definition
Understanding Exterior Angle Sum
Exterior Angle Sum is the total of one exterior angle at each vertex of a polygon, taken in a consistent direction around the figure. The exterior angles of a polygon always add to 360 degrees. That total is always three hundred sixty degrees.
A useful way to understand the rule is to imagine walking around the polygon. Each exterior angle is a turning amount, and one complete trip around the boundary brings you back to your starting direction after a full turn.
This fact works for regular and irregular polygons. In a regular n-gon, it becomes especially simple because each exterior angle has the same measure, so each one is three hundred sixty divided by n.
Key facts
Important ideas to remember
- The exterior angles of a polygon always add to 360 degrees.
- The sum of one exterior angle per vertex is always three hundred sixty degrees.
- The rule works for regular and irregular polygons when the exterior angles are taken consistently around the shape.
- In a regular polygon, each exterior angle equals 360 divided by n.
Where it is used
Where exterior angle sum shows up
- Use the exterior-angle sum rule to find one exterior angle of a regular polygon.
- Use it to solve for the number of sides in regular polygon problems.
- Use it to connect polygon geometry with the idea of a full turn or rotation.
Common mistakes
What to watch out for
- Do not add both possible exterior angles at each vertex; use one consistent set around the polygon.
- Do not confuse the exterior-angle sum with the interior-angle sum, which depends on n.
- Do not assume the rule gives one exterior angle unless the polygon is regular.