###### Consider the angle sum of a quadrilateral.
Clearly, the diagonal *AC* divides the quadrilateral into 2
triangles.
Consider the angle sum of a pentagon.
Clearly, the diagonals *AC *and *AD* divides the pentagon into
3 triangles.
Consider the angle sum of a hexagon.
Clearly, the diagonals *AC*, *AD*, and *AE* divides the
hexagon into 4 triangles.
From the above discussion, we observed that:
In general:
Note that a polygon of *n *sides is called an* n*-gon.
External Angle Sum of Polygons
Let the exterior angles of a triangle be rearranged so that they have the
same vertex as shown above.
Let us now consider the external angle sum of a rectangle.
Let the exterior angles of a rectangle be rearranged so that they have
the same vertex as shown above.
In general:
The external angle sum of a polygon is 360º.
Example 1
Calculate the exterior and interior angle of a regular pentagon.
##### Solution:
A regular pentagon has five equal angles.
Let the interior angle be *x*º.
So, each interior angle is 108º.
Key Terms
(internal) angle sum of a polygon, external
angle sum of a polygon |