Explanation
In this page, we look at more examples of regular polygons and their exterior angles.
The key idea is:
When we go around a regular polygon, the exterior angles make one full turn.
One full turn is:
\(360^\circ\)
So, the sum of the exterior angles is always:
\(360^\circ\)
For a regular polygon, all exterior angles are equal. So we can divide 360° by the number of sides to find each exterior angle.
Formula / Rule
For any regular polygon:
Sum of Exterior Angles \(= 360^\circ\)
For each exterior angle:
Each Exterior Angle \(= \frac{360^\circ}{n}\)
where:
\(n\) is the number of sides of the regular polygon.
Example 1
Find the sum of the exterior angles of a regular triangle.
A regular triangle has \(3\) equal exterior angles.
The sum of the exterior angles is:
\(360^\circ\)
So, the sum is:
\(360^\circ\)
To find each exterior angle:
Each Exterior Angle \(= \frac{360^\circ}{3}\)
\(= 120^\circ\)
So, each exterior angle of a regular triangle is:
\(120^\circ\)
And:
\(120^\circ + 120^\circ + 120^\circ = 360^\circ\)
Example 2
Find the sum of the exterior angles of a square.
A square has \(4\) equal exterior angles.
The sum of the exterior angles is:
\(360^\circ\)
To find each exterior angle:
Each Exterior Angle \(= \frac{360^\circ}{4}\)
\(= 90^\circ\)
So, each exterior angle of a square is:
\(90^\circ\)
And:
\(90^\circ + 90^\circ + 90^\circ + 90^\circ = 360^\circ\)
Example 3
Find the sum of the exterior angles of a regular pentagon.
A regular pentagon has \(5\) equal exterior angles.
The sum of the exterior angles is:
\(360^\circ\)
To find each exterior angle:
Each Exterior Angle \(= \frac{360^\circ}{5}\)
\(= 72^\circ\)
So, each exterior angle of a regular pentagon is:
\(72^\circ\)
And:
\(72^\circ + 72^\circ + 72^\circ + 72^\circ + 72^\circ = 360^\circ\)
Example 4
Find each exterior angle of a regular hexagon.
A regular hexagon has 6 sides, so:
\(n = 6\)
Use the formula:
Each Exterior Angle \(= \frac{360^\circ}{n}\)
Substitute:
Each Exterior Angle \(= \frac{360^\circ}{6}\)
\(= 60^\circ\)
So, each exterior angle of a regular hexagon is:
\(60^\circ\)
The sum of all exterior angles is still:
\(360^\circ\)
Example 5
Find each exterior angle of a regular octagon.
A regular octagon has \(8\) sides, so:
\(n = 8\)
Use the formula:
Each Exterior Angle \(= \frac{360^\circ}{n}\)
Substitute:
Each Exterior Angle \(= \frac{360^\circ}{8}\)
\(= 45^\circ\)
So, each exterior angle of a regular octagon is:
\(45^\circ\)
The sum of all exterior angles is:
\(360^\circ\)
Practice
- More Examples (Current page)
Continue Learning
- Sum of Exterior Angles of Regular Polygons (Proof)
- Sum of Exterior Angles of Convex Polygons (Proof)