The word polygon

is a combination of two Greek words: “poly” means many and “gon”

means angle. Along with its angles, a polygon also has sides and vertices.

“Tri” means “three,” so the simplest polygon is called

the triangle, because it has three angles. It also has three sides and three

vertices. A triangle is always coplanar, which is not true of many of the

other polygons.

A regular polygon

is a polygon with all angles and all sides congruent, or equal. Here are some

regular polygons.

We can use a

formula to find the sum of the interior angles of any polygon. In this formula,

the letter n stands for the number of sides, or angles, that the polygon has.

**sum
of angles = (n 2)180°**

Let’s use the

formula to find the sum of the interior angles of a triangle. Substitute 3

for n. We find that the sum is 180 degrees. This is an important fact to remember.

**sum
of angles = (n 2)180°
= (3 2)180° = (1)180° = 180° **

To find the

sum of the interior angles of a quadrilateral, we can use the formula again.

This time, substitute 4 for n. We find that the sum of the interior angles

of a quadrilateral is 360 degrees.

**sum
of angles = (n 2)180°
= (4 2)180° = (2)180° = 360°**

Polygons can

be separated into triangles by drawing all the diagonals that can be drawn

from one single vertex. Let’s try it with the quadrilateral shown here. From

vertex A, we can draw only one diagonal, to vertex D. A quadrilateral can

therefore be separated into two triangles.

If you look

back at the formula, you’ll see that n 2 gives the number of triangles

in the polygon, and that number is multiplied by 180, the sum of the measures

of all the interior angles in a triangle. Do you see where the “n

2” comes from? It gives us the number of triangles in the polygon. How

many triangles do you think a 5-sided polygon will have?

Here’s a pentagon,

a 5-sided polygon. From vertex A we can draw two diagonals which separates

the pentagon into three triangles. We multiply 3 times 180 degrees to find

the sum of all the interior angles of a pentagon, which is 540 degrees.

**sum
of angles = (n 2)180°
= (5 2)180° = (3)180° = 540°**

**Related Links:**

Polygon definitions,

p olygon formulas (area, perimeter) and polygon names (Tables and Formulas)