Polygons are named according to their number of line segments,
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.)
Try an interactive Java applet that allows you to interactively set the size of angle.
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°.
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.
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).