# Polygon Angle Calculator

If you want to **calculate the interior and exterior angles of polygons** that are regular, the polygon angle calculator can help you. Enter the numbers straight away or read on to learn how to calculate angles in a polygon.

If you're unfamiliar with the difference between the interior and exterior angles of polygons, don't worry - we'll cover that too!

## Interior and exterior angles of polygons

Before we learn how to calculate angles in a polygon, it's worth knowing what exactly we can determine. The two most important types are:

**Interior polygon angles**- These lie inside the polygon at its vertices.**Exterior polygon angles**- They are defined outside the polygon between one of its sides and the extension of an adjacent side.

**In regular polygons** whose sides all have the same length, **the angles of the same type are equal.**

## How to find the interior angle of a polygon?

For a regular polygon with $n$ sides, the interior angle, $\alpha$, can be found using the formula:

🔎 The **numerator** in this formula gives you the sum of interior angles in a polygon.

## Formula to calculate the exterior angle of a polygon

You can calculate the exterior angle of a polygon, $\beta$, using the following equation:

It may be helpful to remember that **the exterior and interior polygon angles sum up to 180°**. Therefore, you can write:

where we used the fact that $2\pi = 180\degree$. Feel free to brush up on the angle conversion if there's any confusion! Both radians and degrees are fine to use but remember to **keep the units consistent**.

You can also save yourself the hassle and use the polygon angle calculator, which allows easy conversion between the units.

## Other calculators about polygons

If you'd like to do more than calculate the interior and exterior angles of polygons, we've got plenty of tools that can assist you:

- Regular polygon calculator;
- Area of regular polygon calculator;
- Heptagon calculator;
- Heptagon area calculator;
- Dodecagon calculator;
- Dodecagon area calculator;
- Decagon calculator;
- Decagon area calculator; and
- Hexagon calculator.

## FAQ

### How do I find the interior angle of a regular polygon?

You can calculate the interior angles of a regular polygon as follows:

- Determine the
**number of sides**,`n`

. **Subtract 2**from`n`

.- Multiply the difference by
`π`

. - Divide the result by
`n`

- this is the**magnitude of the interior polygon angles**.

### What regular polygon has an exterior angle of 60 degrees?

A **regular hexagon** has an exterior angle of 60°. Exterior angles always sum up to 360°. Dividing it by 60° gives 6 - the number of sides in a hexagon.

### How many angles does a regular polygon have?

Regular polygons have **as many angles as sides**, both interior and exterior. For example, a pentagon has 5 sides, 5 interior angles, and 5 exterior angles.

### Which regular polygon will have the largest angle measure?

An **equilateral triangle has the largest exterior angle**, 120°.

For an interior angle, the limit is 180°, which is approached as the number of sides tends to infinity.