Angles in Polygons

Knowing the sum of the measure of the angles of a triangle is 180° can help us determine the sum of the measure of the angles of any polygon. Any polygon can be divided into triangles. By multiplying the number of triangles in a polygon by 180°, we can determine the sum of the measure of the angles.

For example, the square can be divided into 2 triangles. 2 times 180° = 360°. Therefore the sum of the measure of the angles of a square is 360°.

Using the line segment tool, determine the number of triangles each of the remaining polygons can be divided into, then determine the sum of the angles in each polygon.

Do you see a relation between the number of sides in a polygon and the number of triangles in the polygon?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Michael Smith, Created with GeoGebra