Polygon: Interior Angles
How to solve the interior angles of a polygon: formula, 2 examples, and their solutions.
Polygon Names
These are the commonly used polygons.
Tri-: 3
Quadri-: 4
Penta-: 5
Hexa-: 6
Hepta-: 7
Octa-: 8
Nona-: 9
Deca-: 10
Formula
For an n-gon,
the sum of the measures
of the interior angles is
(sum) = 180(n - 2).
Example
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
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.
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.