3.5 Polygon Angle Sum Theorem
October 09, 2009
3­5 Polygon Angle Sum Theorem
Objectives
Explore the patterns found in the angles of polygons.
Identify formulas for finding interior and exterior angles of a polygon.
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3.5 Polygon Angle Sum Theorem
October 09, 2009
EXPLORATION
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3.5 Polygon Angle Sum Theorem
Number of sides (n)
October 09, 2009
Number of triangles formed
Sum of interior angles
Sum of exterior angles
4
5
6
7
8
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3.5 Polygon Angle Sum Theorem
October 09, 2009
4 sides
5 sides
6 sides
___ triangles
___ triangles
___ triangles
7 sides = ___ triangles
8 sides = ___ triangles
A triangle has 180 degrees,
so multiply the number of triangles by 180.
n sides = _____ triangles
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3.5 Polygon Angle Sum Theorem
Number of sides (n)
October 09, 2009
Number of triangles (n­2)
Sum of interior angles
(n­2)180
4
(4­2) = 2
(4­2)180 = 360
5
(5­2) = 3
(5­2)180 = 540
6
(6­2) = 4
(6­2)180 = 720
7
(7­2) = 5
(7­2)180 = 900
8
(8­2) = 6
(8­2)180 = 1080
n
(n­2) = (n­2)180 =
Sum of exterior angles
Nov 12­7:52 AM
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3.5 Polygon Angle Sum Theorem
Number of sides (n)
October 09, 2009
Number of triangles (n­2)
Sum of interior angles
(n­2)180
4
(4­2) = 2
(4­2)180 = 360
5
(5­2) = 3
(5­2)180 = 540
6
(6­2) = 4
(6­2)180 = 720
7
(7­2) = 5
(7­2)180 = 900
8
(8­2) = 6
(8­2)180 = 1080
n
(n­2) = (n­2)180 =
Sum of exterior angles
ALWAYS
360
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3.5 Polygon Angle Sum Theorem
October 09, 2009
So, how many interior degrees are in a 43­gon?
How about a 100­gon?
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3.5 Polygon Angle Sum Theorem
October 09, 2009
So, if I had a REGULAR pentagon, how many degrees would be in ONE interior angle?
540/5 = 108 degrees in each interior angle
IMPORTANT FORMULA
The number of degrees in ONE interior angle of a REGULAR polygon is defined as:
A REGULAR POLYGON is a polygon where all the sides and angles are equal.
(n­2) 180
n
where n is the number of sides
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3.5 Polygon Angle Sum Theorem
RECAP:
October 09, 2009
In a polygon with n sides,
How many triangles are in the figure?
(n­2)
How many total degrees are on the interior?
(n­2)180
How many degrees are in ONE interior angle if the polygon is regular?
(n­2) 180
How many degrees are there on the exterior of the polygon?
n
360
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3.5 Polygon Angle Sum Theorem
October 09, 2009
HOMEWORK
p. 161 #11­25
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Attachments
CarpineK_final%20project[1].gsp