Explanation:
In geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite
sequence of straight line
segments (i.e., by a closed polygonal chain). These
segments are called its edges or sides,
and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. An n-gon is a polygon with n sides. The interior of the polygon is
sometimes called its body.
A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.
The word "polygon" derives from the Greek"much", "many" and
"corner" or "angle". Today a polygon is more usually
understood in terms of sides.
Properties
Angles
Any polygon, regular or irregular,
self-intersecting or simple, has as many corners as it has sides. Each corner
has several angles. The two most important ones are:
Interior angle - The sum of the
interior angles of a simple n-gon is (n − 2)
π radians or (n − 2)180 degrees. This is because
any simple n-gon can be considered
to be made up of (n − 2) triangles, each of which has an
angle sum of π radians or 180 degrees. The measure of any interior angle
of a convex regular n-gon is radians or degrees. The interior
angles of regular star polygons were first studied by Poinsot, in the same paper in which he
describes the four regular star polyhedra.
Exterior angle - Imagine walking
around a simple n-gon marked on the
floor. The amount you "turn" at a corner is the exterior or external
angle. Walking all the way round the polygon, you make one full turn, so the
sum of the exterior angles must be 360°.(Our solved example in mathguru.com uses
this concept)
Moving around an n-gon in general, the sum
of the exterior angles (the total amount one "turns" at the vertices)
can be any integer multiple d of 360°, e.g. 720° for a pentagram and 0° for an angular
"eight", where d is the density or starriness of the polygon.
http://en.wikipedia.org/wiki/Polygon
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.