External angles law

In geometry, an interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. A simple polygon has exactly one internal angle per vertex. Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. ... A simple concave hexagon In geometry, two edges of a polygon may cross or even overlap in general. ... In geometry, a vertex (plural vertices) is a special kind of point, usually a corner of a polygon, polyhedron, or higher dimensional polytope. ...

If every internal angle of a polygon is at most 180 degrees, the polygon is called convex. A convex pentagon In geometry, a convex polygon is a simple polygon whose interior is a convex set. ...

Interior Angle Measures of Regular Polygons

To find the total measure of degrees in a regular polygon, (regular meaning all sides and angles are equal) you must take the number of sides the polygon has, n, subtract 2 from it, then multiply that number by 180.

Example:

A decagon, a polygon with 10 sides, is a simple shape to figure the total measure of.

= Measure in Degrees, when n = number of sides

Solution to the decagon:

The total measure of the decagon is 1440º.

Divide that number by the number of sides, in this case, 10, to find the measure of each angle.

Each interior angle of a regular decagon is 144º.

Finding the Exterior Angles on a Regular Polygon

This is one of the simplest theorems to memorize in all of science and litracy .

The sum of all the exterior angles on a polygon is 360º.

To find the measure of a regular decagon's exterior angles, divide 360 by the number of sides the polygon has, in this case, 10.

So all the exterior angles in a regular decagon are 36º.

External links

• Internal angles of a triangle and External angles of a triangle With interactive animation
• Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference