Exterior Angles of Polygons
Exterior angles of any convex polygon sum to 360°.
Key idea
Exterior angles of any convex polygon sum to 360°.
In depth
Walking around any convex polygon, you turn through a total of 360°, so the exterior angles always sum to 360°. Each exterior angle of a regular polygon is 360°/n.
Worked example
A regular octagon has exterior angle 360/8 = 45°, so each interior angle is 135°.
Real-world uses
- Planning a turning path for a robot or a running course around a polygon
Common mistake
Thinking the sum of exterior angles depends on the number of sides.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Exterior Angles of Polygons?
Exterior angles of any convex polygon sum to 360°. It is a topic at the intermediate level in Geometry.
Where is Exterior Angles of Polygons used in real life?
Real-world examples: Planning a turning path for a robot or a running course around a polygon.
What should I learn before Exterior Angles of Polygons?
Make sure you are comfortable with Interior Angles of Polygons, the previous topic in Geometry.
What is a common mistake with Exterior Angles of Polygons?
Thinking the sum of exterior angles depends on the number of sides.
How can I practise Exterior Angles of Polygons?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Exterior Angles of Polygons?
Move on to Regular Polygon Area next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.