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.