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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 $540^{\circ}$.


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

1. Draw circle $O$ (red).

2. Draw diameter $AB$ and construct a perpendicular radius through $O$.

3. Construct the midpoint of $CO$, and label it $E$.

4. Draw $AE$ (green).

5. Construct the angle bisector of $\angle AEO$, and label its intersection with $AB$ as $F$ (pink).

6. Construct a perpendicular to $AB$ at $F$.

7. Adjust your compass to length $AG$, and mark off points $H$, $I$ and $J$ on circle $O$.

8. $AGHIJ$ is a regular pentagon.

See also

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