Year 8 Interactive Maths - Second Edition

Internal Angle Sum of Polygons

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