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 xº.
So, each interior angle is 108º.
Key Terms
(internal) angle sum of a polygon, external
angle sum of a polygon
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