### 6.1_Angles_of_Polygons_web

```"The main difference between a cat and a lie is that a cat only has nine lives." Mark Twain
Chapter 6 Definitions
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Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Diagonal
Base
Legs
Objective: Apply the Angle Sum Theorem for polygons to find interior and exterior angle
measures given the number of sides, to find the number of sides given angle measures,
and to solve contextual problems.
Interior Angles of Polygons
180
180
180+ 180= 360
180
180
180
180+ 180 + 180 = 540
180
180
180
180
180+ 180 + 180 + 180 = 720
180+180+ 180 + 180 + 180 = 900
Interior Angles Sum Theoreom
Convex Polygon
# of Sides
# of Triangles
Sum of Angle
Measures
Triangle
3
1
180
4
2
360
Pentagon
5
3
540
Hexagon
6
4
720
Heptagon
7
5
900
Octagon
8
6
1080
Polygon
N
(n-2)
180(n-2)
If a convex polygon has n sides and S is the sum of the
measures of its interior angles then S=180(n-2)
Application – Regular Polygon
• The benzene molecule C6H6 consists of six carbon atoms
in a regular hexagonal pattern with a hydrogen atom
attached to each carbon atom. Find the sum of the
measures of the interior angles of the hexagon.
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Convex Polygon
S=180(n-2)
S=180(6-2)
S=180(4)
S=720
Application –
Regular Polygon
• A mall is designed so the five walkways meet at a food
court that is in the shape of a regular pentagon. Find the
sum of the measures of the interior angles of the
pentagon.
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Convex Polygon
S=180(n-2)
S=180(5-2)
S=180(3)
S=540
Irregular Polygon
C
B
2x
x
A
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2x
x
D
Find the measures of the angles.
360=mA + mB +mC + mD
360 = x + 2x +2x + x
360 = 6x
x = 60
mA & mD = 60, mB & mC = 180
Exterior Angle Sum Theorem
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If a polygon is convex, then the sum of the measure of the exterior angles, one at
each vertex is 360
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Exterior Angles
• Find the measures of an exterior
angle and an interior angle of
the convex regular octagon
ABCDEFGH
Interior Angles
S=180(n-2) Individual Interior Angles
S=180(6)
S=1080/8
Exterior Angles
S=1080
= 135
360/8 = 45
Note Exterior & Interior Angle are a Linear Pair
(supplementary) 135+45 = 180
Summary
• For Convex Polygons
• Measure of Interior Angles =
180(n-2)
• Measure of Exterior Angles =
360
Practice Assignment
Block Page 394 12 - 32 even
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