How to Calculate Interior Angles of Polygons

Miacademy & MiaPrep Learning Channel

This video provides a step-by-step guide to understanding and calculating the interior angles of polygons. It begins by guiding viewers through a discovery process where they divide various polygons into triangles using diagonals, revealing the underlying pattern that connects the number of sides to the total sum of interior angles. This process leads naturally to the derivation of the formula (n-2)180, empowering students to understand the origin of the math rather than simply memorizing a rule. The video explores key geometric concepts including vertices, diagonals, regular versus irregular polygons, and the distinction between finding the sum of angles versus finding the measure of a single angle. It specifically addresses the conditions required to calculate a single interior angle—namely, that the polygon must be regular (equiangular and equilateral). The narrator uses visual examples, including a decagon, to demonstrate these concepts in practice. For educators, this resource is excellent for introducing the interior angle sum theorem in a Geometry unit. It encourages critical thinking by asking students to predict patterns and verify formulas. The clear distinction made between the sum of angles (applicable to all convex polygons) and the measure of individual angles (applicable only to regular polygons) helps prevent a common student misconception. The video is designed to be interactive, with specific prompts for students to pause and check their notes.