Angles of Polygons
To find the sum of angles in a polygon, you can simply use the following formula:
where n is the number of sides
For example, a triangle has three sides therefore the total sum of angles is:
How about a 4-sided polygon (also called quadrilaterals)?
This could go on and on...
In fact, a table could be made here...
|Polygon||Sides||Sum of Angles|
...of course, the number of polygons does not stop here. However, there is an ever increasing pattern of 180° per one side added.
In addition, for any regular polygon, dividing the sum of angles by the number of sides (or vertices) would result in the angle of each vertex. A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or concave.
1. Find the sum of angles of a regular polygon that has 15 sides (pentadecagon):
2. Find the angle on a vertex of a regular pentadecagon: