Unit A: Geometry

Chapter 1: Polygons

The Sum of the Interior Angles in a Polygon

An example of a regular pentagon is below.

Each side is 3 cm, and each angle measures 108°.

How can the sum of the interior angles be found in a regular polygon?

To find out, view the video Sum of Angles.

The Sum of the Interior Angles in a Polygon

As seen in the video, the equation for the sum of the interior angles in a polygon is S = 180°(n–2), where S is the sum of the interior angles and n is the number of sides.

Example 2

Find the sum of the interior angles of a 16-sided figure without making a sketch.

Hint: Don’t forget to use BEDMAS. The operation in the brackets must be completed first.

\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (16 - 2) \\ = & 180 ° (14) \\ = & 2 520 ° \end{array}

Example 3

Determine the sum of the interior angles of a 30-sided figure.

\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (30 - 2) \\ = & 180 ° (28) \\ = & 5 040 ° \end{array}