Polygons and Angles

 1. General Information 2. Angles of Polygons

General Information
Polygons are closed plane figures bounded by three or more line segments. Polygons cannot be composed of any curves since true curves cannot be constructed using straight line segments. Circles and ellipses, therefore, are not polygons.

Polygons are named according to their number of line segments, or sides.

 Examples of polygons
 name number of sides triangle 3 quadrilateral 4 pentagon 5 hexagon 6 heptagon 7 octagon 8 nonagon 9 decagon 10 11-gon 11 dodecagon 12 ... ... n-gon n

How to name polygons

A point at which two adjacent sides in a polygon meet is called a vertex. These two adjacent sides and the vertex define an angle. The measure of an angle refers to the amount of rotation needed to superimpose one of the line segments onto the other. The unit used to measure angles is the degree (°). There are 360 degrees in one full circle rotation. (Note: angles having ninety degrees are also known as right angles.)

 A general angle
 Angle measures are based on a 360 degree scale

Try an interactive Java applet that allows you to interactively set the size of angle.

 1. General Information 2. Angles of Polygons
Angles of Polygons
When we refer to the angles of a polygon, we are in fact referring to interior angles. An important property of polygons is that all polygons with the same number of sides have the same sum of interior angles. For example, adding the three interior angles of any triangle (three-sided polygon) always produces 180°.

 The three interior angles of any triangle sum to 180°

Furthermore, adding the four angles of any quadrilateral always produces 360°, and adding the five angles of any pentagon always produces 540°. In general, adding the interior angles of any n-sided polygon always produces 180(n-2) degrees. Why does this pattern occur?

Every time we add another side to a polygon, a triangle is in effect added on to the polygon. Since the angles of a triangle total 180 degrees, 180 degrees are added to the interior angle sum of the polygon.

 Adding a side to a polygon is equivalent to adding a triangle to the polygon

In summary, every three-sided polygon has an interior angle sum of 180°. For every side more than 3, 180 degrees is added to the sum. Thus, the interior angle sum of a polygon with n sides is 180°(n-2).

Web Resource
For an exploration of polygons using tangrams, visit a site called "Tangrams".