6.2. Exterior Angles in Convex Polygons http://www.ck12.org
6.2 Exterior Angles in Convex Polygons
Here you’ll learn the Exterior Angle Sum Theorem that states that the exterior angles of a polygon always add up to
360 ◦.
What if you were given a twelve-sided regular polygon? How could you determine the measure of each of its exterior
angles? After completing this Concept, you’ll be able to use the Exterior Angle Sum Theorem to solve problems
like this one.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter6ExteriorAnglesinConvexPolygonsA
Watch the second half of this video.
MEDIA
Click image to the left for more content.James Sousa:Angles of Convex Polygons
Guidance
Recall that anexterior angleis an angle on the outside of a polygon and is formed by extending a side of the
polygon.
As you can see, there are two sets of exterior angles for any vertex on a polygon. It does not matter which set you
use because one set is just the vertical angles of the other, making the measurement equal. In the picture above, the
color-matched angles are vertical angles and congruent. TheExterior Angle Sum Theoremstated that the exterior
angles of a triangle add up to 360◦. Let’s extend this theorem to all polygons.
Investigation: Exterior Angle Tear-Up
Tools Needed: pencil, paper, colored pencils, scissors
- Draw a hexagon like the hexagons above. Color in the exterior angles as well.
- Cut out each exterior angle and label them 1-6.
- Fit the six angles together by putting their vertices together. What happens?