# 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
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

### 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.

## Example 2

### 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.