geo 6­1.notebook
6-1, Angles of Polygons
Today you will...
January 03, 2013
Polygon Interior Angles Sum
A diagonal of a polygon is a segment that connects any two
nonconsecutive vertices.
- Find and use the sum of the measures of the interior angles
of a polygon.
- Find and use the sum of the measures of the exterior angles
of a polygon.
Since the sum of the angle measures of a triangle is 180, we can make
a table and look for a pattern to find the sum of the angle measures
for any convex polygon.
This leads to the following theorem.
You can use the Polygon Interior Angles Sum Theorem to find the sum
of the interior angles of a polygon and to find missing measures in
polygons.
geo 6­1.notebook
January 03, 2013
Find the sum of the measures of the interior angles of a convex
octagon.
Find the measure of each interior angle of pentagon HJKLM shown.
Recall that in a regular polygon, all of the interior angles are congruent.
You can use this fact and the Polygon Interior Angle Sum Theorem to
find the interior angle measure of any regular polygon.
Find the measure of each interior angle of the regular 11-gon that
appears on the face of a Susan B. Anthony one-dollar coin.
A certain company makes hot tubs in a variety of different shapes.
Find the measure of each interior angle of the nonagon model.
Given the interior angle measure of a regular polygon, you can also use
the Polygon Interior Angles Sum Theorem to find a polygon's number
of sides.
geo 6­1.notebook
January 03, 2013
The measure of an interior angle of a regular polygon is 150. Find the
number of sides in the polygon.
The measure of an interior angle of a regular polygon is 144. Find the
number of sides in the polygon.
Polygon Exterior Angles Sum
Does a relationship exist between the number of sides of a convex
polygon and the sum of its exterior angle measures? Examine the
polygons below in which an exterior angle has been measured at each
vertex.
Find the value of x in the diagram.
Find the measure of each exterior angle of a regular dodecagon.