Definition:Polygon

A polygon is a closed plane figure made up of an unspecified number of lines:



Side
The lines which make up the polygon are known as its sides.

Thus, in the diagram above, the sides are $$a, b, c, d$$ and $$e$$.

Vertex
The corners of a polygon are known as its vertices (singular: "vertex").

Thus, in the diagram above, the vertices are $$A, B, C, D$$ and $$E$$.

Adjacent
Each vertex is formed by the intersection of two sides.

The two sides that form a particular vertex are referred to as the adjacents of that vertex, or described as adjacent to that vertex.

Similarly, each side of a polygon intersects two other sides, and so is terminated at either end by two vertices.

The two vertices that terminate a particular side are referred to as the adjacents of that side, or described as adjacent to that side.

Internal Angle
The internal angle (or "interior angle") of a vertex is the size of the angle between the sides forming that vertex, as measured inside the polygon.

External Angle
Surprisingly, the external angle (or "exterior angle") of a vertex is not the size of the angle between the sides forming that vertex, as measured outside the polygon.

It is in fact an angle formed by one side of a polygon and a line extended from an adjacent side:



While $$\angle AFE$$ is the internal angle of vertex $$F$$, the external angle of this vertex is $$\angle EFG$$.

Regular Polygon
A regular polygon is a polygon in which all the sides are the same length, and all the vertices have the same angle:



Note
The vertices and the sizes of the internal angles of those vertices are frequently referred to by the same letter.

Thus "the angle of vertex $$A$$" is called "angle $$A$$" or "$$\angle A$$".

This is considered by some to be an abuse of notation but its convenience outweighs its disadvantages.