6.1. Angles in Polygons http://www.ck12.org
Interior Angles in Convex Polygons
Recall from Chapter 4, that interior angles are the angles inside a closed figure with straight sides. Even though this
concept was introduced with triangles, it can be extended to any polygon. As you can see in the images below, a
polygon has the same number of interior angles as it does sides.
From Chapter 1, we learned that a diagonal connects two non-adjacent vertices of a convex polygon. Also, recall
that the sum of the angles in a triangle is 180◦. What about other polygons?
Investigation 6-1: Polygon Sum Formula
Tools Needed: paper, pencil, ruler, colored pencils (optional)
- Draw a quadrilateral, pentagon, and hexagon.
- Cut each polygon into triangles by drawing all the diagonals from one vertex. Count the number of triangles.