Unit 8 · Polygons and Quadrilaterals

8.1Polygon Angle Sums

Quick Answer

Interior angle sum of an n-gon = (n−2)×180°. Each interior angle of a regular n-gon = (n−2)×180°/n. The sum of exterior angles of any convex polygon is always 360°.

Essential Question

Why does the interior angle sum of a polygon increase by 180° for each additional side, and why is the exterior angle sum always 360°?

Learning Goals

  • 1State the Polygon Interior Angle Sum Theorem.
  • 2Find the interior angle sum of any polygon.
  • 3Find each interior angle of a regular polygon.
  • 4State and apply the Exterior Angle Sum Theorem.

Key Vocabulary

Interior Angle Sum Theorem

Sum of interior angles of an n-gon = (n−2)×180°.

Exterior Angle Sum Theorem

The sum of the exterior angles of any convex polygon is 360°.

Regular polygon

A polygon with all sides congruent and all angles congruent.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.