# Angles in polygons

The interior angles of a polygon with n sides add up to (n - 2) x 180 degrees. The outside (exterior) angles always add up to 360 degrees.

Maths (school) · Part 05: Angles and area · Card 3 of 8 · Last updated 2026-10-19

## Analogy

Like cutting a shape into triangles from one corner, each worth 180 degrees.

## Example

**Regular hexagon**

Sum = (6 - 2) x 180 = 720
Each angle = 720 / 6 = 120
Exterior = 360 / 6 = 60

## In practice

Floor tilers need to know a hexagon's angle is 120 degrees so tiles fit without gaps.

## Practice

### Flashcards

- **What is the sum of interior angles in a hexagon?** 720 degrees, from (6 - 2) x 180.

### Interview questions

**Calculate the interior angle of a regular hexagon and explain your method.**

- A hexagon splits into 4 triangles
- Sum of angles = 4 x 180 = 720
- Divide by 6 equal angles
- Each angle is 120 degrees

## Questions people ask

### Why is the sum (n - 2) x 180 degrees?

From one corner, you can draw lines to split any polygon into n - 2 triangles. Each triangle has angles adding to 180 degrees. A hexagon has 6 sides, so it splits into 4 triangles, giving 4 x 180 = 720 degrees in total.

### What is a regular polygon?

A regular polygon has all sides the same length and all angles the same size. A square and an equilateral triangle are regular. A rectangle is not, because its sides are not all equal. In a regular polygon each exterior angle is 360 divided by n.

## Related concepts

- [Angle rules](https://studyvisually.com/learn/science/maths-school/maths-school-part-5/maths-school-part-5-concept-1)
- [Angles in parallel lines](https://studyvisually.com/learn/science/maths-school/maths-school-part-5/maths-school-part-5-concept-2)
- [Circle theorems](https://studyvisually.com/learn/science/maths-school/maths-school-part-5/maths-school-part-5-concept-8)

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