GMAT Exam: A Simple Guide To Geometry - Polygons

Descriptions of Polygons
A polygon is a simple, closed plane figure composed of sides that are straight line segments that meet only at their endpoints.
The point at which the two sides of a polygon intersect is a vertex.
A diagonal is a line segment that connects two nonconsecutive vertices.

Polygons are named by the number of sides they have.
A triangle is a three-sided polygon.
A quadrilateral is a four-sided polygon.
A pentagon is a five-sided polygon.
A hexagon is a six-sided polygon.
A heptagon is a seven-sided polygon.
An octagon is an eight-sided polygon.

Other polygons with additional sides have special names as well.
However, eventually, at a high number of sides, you simply speak of the polygon as an n-gon.
A regular polygon has all sides and angles congruent.

Interior and Exterior Angles
An n-sided polygon has n interior angles and n exterior angles. The sum of the measures of its interior angles is (n – 2)180°.
The sum of the measures of its exterior angles is 360°, no matter how many sides the polygon has.

An exterior angle of a polygon is the angle between one side of the polygon and the extension of the side adjacent to it.

Here is an example of the interior and exterior angles of a triangle.


There are two congruent exterior angles at each vertex.

Either one is considered the exterior angle at that vertex.