Interior Angles of Polygons
Sum of interior angles depends on number of sides.
Key idea
Sum of interior angles depends on number of sides.
In depth
A polygon with n sides can be split into n − 2 triangles from one vertex, so the interior angles sum to (n − 2) × 180°. A regular polygon divides this equally.
Worked example
A pentagon: (5 − 2) × 180 = 540°, so each angle of a regular pentagon is 108°.
Formula
Real-world uses
- Working out the angle at each corner of a regular garden bed or a pentagonal table
Common mistake
Using n × 180 or forgetting the − 2.
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 Interior Angles of Polygons?
Sum of interior angles depends on number of sides. It is a topic at the intermediate level in Geometry.
What is the formula for Interior Angles of Polygons?
The key formula is S = (n−2)·180°.
Where is Interior Angles of Polygons used in real life?
Real-world examples: Working out the angle at each corner of a regular garden bed or a pentagonal table.
What should I learn before Interior Angles of Polygons?
Make sure you are comfortable with Polygons, the previous topic in Geometry.
What is a common mistake with Interior Angles of Polygons?
Using n × 180 or forgetting the − 2.
How can I practise Interior 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 Interior Angles of Polygons?
Move on to Exterior Angles of Polygons 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~.