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Example: Find Number of Sides of Polygon Given an Exterior Angle

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Explanation:

 

 

Polygon

 

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.