# Free Math Interactive | Exploring Angle Sums

This middle school level math interactive was developed for NCTM’s Illuminations website to help children learn about the relationship between the number of sides and the sum of the interior angles of polygons.

Children start by selecting a polygon (triangle, quadrilateral, pentagon, hexagon, heptagon or octagon) located in the lower part of the screen.

They can then click and drag the vertices to reshape it. As the figure changes, the angle measures will automatically update in the table on the right.

For triangles and quadrilaterals, you can also play an animated movie by clicking on the blue button in the lower right corner. This movie illustrates how the angle sum of a triangle is always 180 degrees and the angle sum of a quadrilateral is always 360 degrees.

Ideas for Exploration:

Ask children to reshape the triangles and quadrilaterals. Have them also play the animated movie by clicking on the blue button in the lower right corner. Ask them if they notice a different result for different shapes.

Have your children then use the applet to examine pentagons, hexagons, heptagons and octagons, too. Ask them if they notice a pattern and ask them to see if they can find a formula that relates the number of sides to the sum of the interior angle measures.