Angle Rules 2

Explore the Angles Inside Polygons

Angle Rules 2 is an interactive geometry activity that helps students study interior angles in different polygons. The main display shows a large shape with its corners clearly labelled. A table beside the shape lists the measure of each interior angle and shows their total.

Players can switch between several polygon types using the buttons along the bottom of the screen. The available choices include a triangle, quadrilateral, pentagon, hexagon, heptagon, and octagon. This makes it easy to compare what happens to the angle total as the number of sides increases.

For example, the triangle shown in the activity has three angles measuring 60 degrees each. The table shows a total of 180 degrees. The interior angles of every triangle add to 180 degrees.

Watch the Angle Total Change

Moving from a triangle to a polygon with more sides introduces more interior angles. The total also becomes larger.

A quadrilateral has an interior-angle sum of 360 degrees. More generally, the sum of the interior angles of a polygon can be found using the rule (number of sides − 2) × 180 degrees.

Angle Rules 2 makes this idea easier to see because the angle values appear beside the shape. Students do not need to imagine the relationship from a formula alone. They can compare the polygon with the numbers shown in the table.

Each angle has its own number and color. The matching colors help connect an angle on the figure with its measurement in the results panel.

See How Polygons Can Be Split into Triangles

Another useful part of Angle Rules 2 is the visual connection between polygons and triangles. A polygon can be divided into triangles, which helps explain why its interior-angle total follows a predictable pattern. A polygon with (n) sides can be split into (n-2) triangles from one suitable vertex.

This approach makes the rule easier to understand instead of simply memorizing it.

Students can move through the different polygon choices and compare their results. A triangle starts at 180 degrees. Shapes with more sides add more triangles and therefore add another 180 degrees to the total each time.

Angle Rules 2 provides a clear visual way to learn about polygons, individual interior angles, and angle sums. It works well for students who understand geometry better when they can see the shape and the measurements together.