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POLYGON PROPERTIES
A. Finding the Interior Angle
B. The Sum of the Interior Angles
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Polygons Menu
Using sides =
Exercises
5 6 7 8 9
Using Formula1 2
IntroductionInterior Angles
Sum of Angles
Exercises 1 2
Triangles Presentation
Methods Two Methods
Interior Angles 1 2 3Revision
1 2 3Sum of Angles
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POLYGON PROPERTIES
Where would you see these triangles and squares?
Were you right?
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POLYGON PROPERTIES
In the high street??
An Octagon??
A Duodecagon??
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The INTERIOR ANGLE of a POLYGON
x
ANGLE atCENTRE
The ANGLE at the CENTRE
always equals the ...
EXTERIORANGLE
EXTERIOR ANGLEINTERIOR
ANGLESo to find the INTERIOR ANGLE
subtract this from ...
180
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The Interior Angle of a Pentagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 5
360o divided by 5 = 72o
Exterior Angle also = 72o
INTERIOR ANGLE = 180 - 72 = 108o
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The Interior Angle of a Hexagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 6
360o divided by 6 = 60o
Exterior Angle also = 60o
INTERIOR ANGLE = 180 - 60 = 120o
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The Interior Angle of a Septagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 7
360o divided by 7 = 51.4o
Exterior Angle also = 51.4o
INTERIOR ANGLE = 180 - 51.4 = 128.6o
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The Interior Angle of an Octagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 8
360o divided by 8 = 45o
Exterior Angle also = 45o
INTERIOR ANGLE = 180 - 45 = 135o
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The Interior Angle of an Nonagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 9
360o divided by 9 = 40o
Exterior Angle also = 40o
INTERIOR ANGLE = 180 - 40 = 140o
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The Interior Angle of an Decagon
Angle at the CENTRE EXTERIOR
ANGLE
INTERIORANGLE
n = 10
360o divided by 10 = 36o
Exterior Angle also = 36o
INTERIOR ANGLE = 180 - 36 = 144o
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INTERIOR ANGLES - EXAMPLES 1
n Angle at Centre
Exterior Angle
Interior Angle
30 30 150
18 18 162
36 36 144
12
20
10
36 10 10 170
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EXAMPLES 2 - any value of “n”
n Angle at Centre
Exterior Angle
Interior Angle
9 40 40 140
18 20 20 160
100 3.6 3.6 176.4
5 72 72 108
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Formula for the INTERIOR ANGLE
Angle at centre =
n
12 10 180 - 10 = 170o
360n 180 - 360
n
360n
Interior Angle = 360n
More Examples
180 -
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Formula for the INTERIOR ANGLE
30 180 - 30 = 150o
45 180 - 45 = 135o
20 180 - 20 = 160o
40 180 - 40 = 140o
5 180 - 5 = 175o
3.6 180 - 3.6 = 176.4o
12
8
18
9
72
100
n 360n 180 - 360
n
More Examples
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Formula for the INTERIOR ANGLE
72 180 - 72 = 108o
36 180 - 36 = 144o
18 180 - 18 = 162o
90 180 - 90 = 90o
12 180 - 12 = 168o
1 180 - 1 = 179o
5
10
20
4
30
360
n 360n 180 - 360
n
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Sum of the INTERIOR ANGLES
Sides 3 4 5
Triangles 1 2 3
Sum of InteriorAngles
180 360 540
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Sum of the INTERIOR ANGLES
Sides 6 7 8
Triangles 4 5 6
Sum of InteriorAngles
720 900 1080
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Sum of the INTERIOR ANGLES
Method 1 Looking at “Triangles”
Method 2 Using a Formula
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Sum of the INTERIOR ANGLES
Method 1 Looking at “Triangles”
Example 10 sides
Picture or sketch the shape
How many triangles?
12
34
5
678
Answer: 8
Sum of Interior Angles = 8 x 180 = 1440o
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Sum of the INTERIOR ANGLES
Method 2 Using a Formula
Sides 3 4 5 6 7 8 9 10
Triangles 1 2 3 4 5 6 7 8
Number of triangles = n - 2( the number of sides - 2 )
FORMULA Sum of Interior Angles = ( n - 2 ) x 180o
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Sum of the INTERIOR ANGLES
Sum of Interior Angles = ( n - 2 ) x 180o
n n - 2 ( n - 2 ) x 180
10 10 x 180 = 1800o
6 6 x 180 = 1080o
15 15 x 180 = 2700o
7 7 x 180 = 1260o
12
8
17
9
102 100 100 x 180 = 18000o
More Examples
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Sum of the INTERIOR ANGLES
Sum of Interior Angles = ( n - 2 ) x 180o
n n - 2 ( n - 2 ) x 180
4 4 x 180 = 720o
20 6 x 180 = 3600o
5 5 x 180 = 900o
8 8 x 180 = 1440o
6
22
7
10
32 30 30 x 180 = 5400o
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INTERIOR ANGLES Revision 1
n Angle at Centre
Exterior Angle
Interior Angle
36 36 144
24 24 156
60 60 120
10
15
6
36 10 10 170
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n Angle at Centre
Exterior Angle
Interior Angle
40 40 140
45 45 135
18 18 162
9
8
20
180 2 2 178
INTERIOR ANGLES Revision 2
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n Angle at Centre
Exterior Angle
Interior Angle
30 30 150
20 20 160
51.4 51.4 128.6
12
18
7
72 5 5 175
INTERIOR ANGLES Revision 3
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Using a Formula Revision 1
Sum of the INTERIOR ANGLES
Sum of Interior Angles = ( n - 2 ) x 180o
n n - 2 ( n - 2 ) x 180
4 4 x 180 = 720o
8 8 x 180 = 1440o
20 20 x 180 = 3600o
3 3 x 180 = 540o
6
10
22
5
52 50 50 x 180 = 9000o
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Using a Formula Revision 2
Sum of the INTERIOR ANGLES
Sum of Interior Angles = ( n - 2 ) x 180o
n n - 2 ( n - 2 ) x 180
9 9 x 180 = 1620o
6 6 x 180 = 1080o
30 30 x 180 = 5400o
2 2 x 180 = 360o
11
8
32
4
7 5 5 x 180 = 900o
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Using a Formula Revision 3
Sum of the INTERIOR ANGLES
Sum of Interior Angles = ( n - 2 ) x 180o
n n - 2 ( n - 2 ) x 180
10 10 x 180 = 1800o
7 7 x 180 = 1260o
30 40 x 180 = 7200o
11 11 x 180 = 1980o
12
9
42
13
7 5 5 x 180 = 900o