Advertisement

Polygons - Pentagons

Properties of pentagons, interior angles of pentagons

Polygons:  Properties of Pentagons

pentagons

red line

Sum of the Interior Angles of a Pentagon:


pentagons
 

To find the sum of the interior angles of a pentagon, divide it up into triangles... There are three triangles...  Because the sum of the angles of each triangle is 180 degrees...  We get

pentagons

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

red line

Regular Pentagons:
The properties of regular pentagons:

pentagons

All sides are the same length (congruent) and all interior angles are the same size (congruent).

To find the measure of the interior angles, we know that the sum of all the angles is 540 degrees (from above)...  And there are five angles...

pentagons

So, the measure of the interior angle of a regular pentagon is 108 degrees.

red line

The measure of the central angles of a regular pentagon:

pentagons

To find the measure of the central angle of a regular pentagon, make a circle in the middle...  A circle is 360 degrees around...  Divide that by five angles...

pentagons

So, the measure of the central angle of a regular pentagon is 72 degrees.