# Polygon: Interior Angles

How to solve the interior angles of a polygon: formula, 2 examples, and their solutions.

## Polygon Names

### Table

These are the commonly used polygons.

Tri-: 3

Quadri-: 4

Penta-: 5

Hexa-: 6

Hepta-: 7

Octa-: 8

Nona-: 9

Deca-: 10

## Formula

### Formula

For an n-gon,

the sum of the measures

of the interior angles is

(sum) = 180(n - 2).

## Example 1

### Example

### Solution

A heptagon has 7 sides and 7 angles.

So n = 7.

Then the sum of the measures

of the interior angles is

180⋅(7 - 2) = 180⋅5.

180⋅5 = 900

Write the unit degree.

So 900º is the answer.

## Example 2

### Example

### Solution

An octagon has 8 sides and 8 angles.

So n = 8.

Then the sum of the measures

of the interior angles is

180⋅(8 - 2) = 180⋅6.

180⋅6 = 1080

The sum of the measures

of the interior angles is

(sum) = 1080.

A regular polygon has the same sides

and the same interior angles.

So a regular octagon has

the same 8 interior angles.

So the measure of an interior angle

of a regular octagon is

(angle) = 1080/8.

1080/8 = 135

Write the unit degree.

So 135º is the answer.

### Figure

This is a regular octagon.

It has the same 8 sides

and the same 8 interior angles.

The measure of an interior angle is 135.