The LessonEach exterior angle of a regular polygon is given by the formula: In this formula, n is the number of sides of the regular polygon.
How to Find the Exterior Angle of a Regular PolygonFinding the exterior angle of a regular polygon is easy.
QuestionWhat is the exterior angle of a regular octagon?
Start with the formula:
Exterior angle = 360° ⁄ nDon't forget: / means ÷.
Substitute the number of sides into the formula. An octagon has 8 sides. In our example, n = 8.
Exterior angle = 360° ÷ 8
Exterior angle = 45°
Answer:The exterior angle of a regular octagon is 45°.
Lesson SlidesThe slider below shows another real example of how to find the exterior angle of a regular octagon.
Why Does the Formula Work?The sum of the exterior angles of a polygon is 360°. There are as many exterior angles as there are sides, n, and they are all equal. The sum is divided by n to find each exterior angle.
In this formula, n is the number of sides of the polygon. This is why the formula works.