1. Chapter 8: Quadrialterals
Section 8.1: Find Angle Measures in Polygons

2. Section 8.1: Find Angle Measures in Polygons
Polygon: Literally means “many angles/sides”
A figure made up of line segments called sides
Must have at least 3 or more sides
The figure must be closed
No two sides may cross

3. Polygon Vertex (Vertices) B C Side CD
Diagonal: a segment that joins two nonconsecutive vertices D A
Polygon ABCD
Take notice that the figure is closed & that the sides do not cross
This is a convex polygon

4. Examples of Non-Polygons
Not Closed
Lines Cross Each Other

5. Section 8.1: Find Angle Measures in Polygons
Convex Polygon: a polygon in which no line that contains a side of the polygon passes through the interior of the polygon
“Normal Looking”
Concave Polygon: A polygon that appears to cave in

6. Draw the following Polygons:
Quadrilateral
Triangle
Pentagon
Hexagon

7. Draw the following Polygons
Heptagon
Octagon
Nonagon

8. Section 8.1: Find Angle Measures in Polygons
Equilateral: A polygon in which all sides are congruent
Equiangular: A polygon in which all angles are congruent
Regular: A polygon that is both equilateral and equiangular

9. Section 8.1: Find Angle Measures in Polygons
Polygon Interior Angle Theorem: The sum of the interior angles of a convex n-gon is:
(n – 2)  180°
Note: To find the measure of each angle in a regular polygon with n sides, use the following formula:
Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°
Note: To find the measure of each exterior angle of a regular polygon with n sides, use the following formula:

10. Section 8.1: Find Angle Measures in Polygons
The following polygons are equilateral. Find the perimeter
12 in
7 cm
If this hexagon is equilateral and its perimeter is 39 in, how long is each side?

11. Section 8.1: Find Angle Measures in Polygons
The polygons are regular. Find the value of x.
144°
60°
(4x – 5)°
(3x – 6)°
128.57°
(4x + 3)°

12. Section 8.1: Find Angle Measures in Polygons
Try together: Pg. 508 Guided Practice Problems #1- 5

13. Section 8.1: Find Angle Measures in Polygons
Homework: Pg. 510 # 3-16 (all)