Students will use their knowledge that the angles of a triangle add to \(180^\circ\) to understand why the interior angles of a simple polygon add up to \((n - 2)180^\circ\). Students will learn both how to derive this formula and how to use it. Here's an excellent derivation of the formula. Students will also consider the special case of regular polygons, and solve problems involving them. One type of problem is to find the number of sides given one interior angle. Another is to find one interior angle given the number of sides. Here's yet another type. After that, students will learn what a regular tessellation is, and why there are exactly three regular tessellations. The proof involves nothing more than finding the interior angle of a regular polygon, and knowing that angles around a point add to \(360^\circ.\) Next, give your students this challenge. After that, give your students this challenge. Finally, give them this one.