Measurement Session 4, Part B: Angles in Polygons

Session 4, Part B:
Angles in Polygons

In This Part: Classifying by Measure | Other Classifications | Measuring Angles
Sums of Angles in Polygons

We determined that the sum of the measures of the angles of a triangle is 180 degrees. Notice in this diagram that the diagonal from one vertex of a quadrilateral to the non-adjacent vertex divides the quadrilateral into two triangles:

The sum of the angle measures of these two triangles is 360 degrees, which is also the sum of the measures of the vertex angles of the quadrilateral. Note 5

Problem B12

a.	Use this technique of drawing diagonals from a vertex to find the sum of the measures of the vertex angles in a regular pentagon (see below). What is the measure of each vertex angle in a regular pentagon?
b.	How many triangles are formed by drawing diagonals from one vertex in a hexagon?
c.	What is the sum of the measures of the vertex angles in a hexagon?
d.	Find a rule that can be used to find the sum of the vertex angles in any polygon.
e.	Can you use your rule to find the measure of a specific angle in any polygon? Why or why not?

Video Segment
In this video segment, the participants explore the sum of the angles in different polygons. Laura demonstrates a method that will work for any polygon.

Can the measure of individual angles be determined based on dividing the polygon into triangles? Why or why not?

If you are using a VCR, you can find this segment on the session video approximately 13 minutes and 10 seconds after the Annenberg Media logo.

Next > Part C: Geo-Logo

Session 4: Index | Notes | Solutions | Video