m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Polygon: A closed figure with three or more sides is called a polygon.
The sum (S) of the measures of the interior angles of a polygon is given by: S=180(n­2)
n = # of sides
Example: A decagon is a 10 sided polygon. What is the sum of all of the interior angles in a decagon?
Ex: Determine the missing measure in the figure shown. 135°
80°
100°
65°
x
1
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Ex: Determine the missing measure:
135°
150°
x°
80°
125°
135°
130°
Sometimes we have the find the number of sides (n) given the sum (S)
Ex: Determine the number of sides of a polygon whose interior angles add up to 1980°
2
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Regular and Irregular polygons
When all sides are equal, it is called a regular polygon. A polygon where all sides are not equal is called irregular.
Examples of regular polygons:
In regular polygons, all interior angles are equal.
3
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
To find the measure of EACH interior angle in a regular polygon, Each interior angle in a regular polygon = S , where S = sum, n = # of n sides
Example: For Superhero Day, Ms. MacDonald has designed a crest for her costume. The hexagon in the crest is regular. Determine the measure of each angle in the hexagon.
4
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Example: Determine the measure of each interior angle in a regular pentadecagon (15 sided polygon).
Sometimes, we have to find n (# of sides) given the interior angle
Each interior angle = Example: The measure of each interior angle in a regular polygon is 144°. How many sides does the polygon have?
5
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Example: Determine the number of sides in a regular polygon where the interior angle is 135°.
Example: Find the measure of w, x. y and z.
z
w
y
x
6
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
Find x:
120°
A)
x
B)
88°
110°
x°
110°
120°
128°
120°
135°
82°
36°
D)
C)
84°
(8x­30)°
105°
120°
(4x+40)°
(6x+10)°
x
121°
(3x+10)°
Page 99 # 1, 2, 3, 6, 7a, 10, 11, 16
7
m2201 chapter 2 section 2.4 polygons 2013.notebook
October 28, 2013
8