Polygon Angle-Sum Theorems and Problems
Explore the Polygon Angle-Sum Theorems, find the sum of interior angle measures for different polygons, and solve related problems. Understand properties of regular polygons and how to calculate interior angle measures using the Polygon Angle-Sum Theorem.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
6-1 The Polygon Angle-Sum Theorems
Polygon Angle-Sum Theorem The sum of the measures of the interior angles of a n-gon is ? 2 180
NUMBER OF SIDES NAME 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon
Problem 1: Finding a Polygon Angle Sum What is the sum of the interior angle measures of a heptagon?
What is the sum of the interior angle measures of a 17-gon?
The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon?
Corollary to the Polygon Angle-Sum Theorem The measure of each interior angle of a regular n-gon is ? 2 180 ?
Problem 2: Using the Polygon Angle-Sum Theorem The common housefly has eyes that consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in on hexagonal facet?
What is the measure of each interior angle in a regular nonagon?
You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of the exterior angles, one at each vertex is 360.
Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For the pentagon
What is the measure of an exterior angle of a regular nonagon?
