Exterior Angles in Regular Polygons
Concept
An exterior angle of a polygon is the angle that is formed between any side of the polygon and a line extended from the next side. Every polygon has interior and exterior angles. The exterior is the term opposite to the interior which means outside. Therefore exterior angles can be found outside the polygon. The sum of the exterior angles of any polygon is equal to 360°. Any flat shape or figure is said to have interior or exterior angles only if it is a closed shape.
Rules
The sum of the exterior angles of every polygon is 360 degrees.
The measure of one of the exterior angles of a regular polygon can be found by dividing 360 degrees by the number of angles (n).
Example
What is the measure of each exterior angle in a regular decagon?
Solution
The sum of the exterior angles of every polygon is 360 degrees.
A decagon has 10 angles, so:
Practice Exterior Angles in Regular Polygons
Practice Problem 1
What is the measure of each exterior angle in a regular triangle?
Practice Problem 2
What is the measure of each exterior angle in a regular pentagon?
Practice Problem 3
What is the measure of each exterior angle in a regular octagon?
Polygon – A closed figure formed by three or more segments called sides.
Interior angle – An angle of a polygon formed by two of its side and is inside the polygon.
Exterior angle – An angle formed by one side and the extension of the adjacent side. It is outside the polygon.
Related Skill
Geometric Proof