© Boardworks Ltd 2001 Menu POLYGON PROPERTIES A.Finding the Interior Angle B.The Sum of the...

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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