Pentagon

In geometry, a pentagon is a polygon with 5 sides. Each angle of a regular pentagon is $108^{\circ}$ . The sum of the internal angles of any pentagon is $540^{\circ}$ .

Construction

It is possible to construct a regular pentagon with compass and straightedge:

Draw circle $O$ (red).
Draw diameter $AB$ and construct a perpendicular radius through $O$ .
Construct the midpoint of $CO$ , and label it $E$ .
Draw $AE$ (green).
Construct the angle bisector of $\angle AEO$ , and label its intersection with $AB$ as $F$ (pink).
Construct a perpendicular to $AB$ at $F$ .
Adjust your compass to length $AG$ , and mark off points $H$ , $I$ and $J$ on circle $O$ .
$AGHIJ$ is a regular pentagon.