Polygons: How Many Sides - Geometry Article
Explore the concept of determining the number of sides of a polygon based on the difference between marked angles in a regular polygon. Learn the calculation method and formula for finding the total sides of an n-gon. Gain insights into polygon geometry with illustrations and explanations in this mathematics teaching article by Paul Stephenson.
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Presentation Transcript
How Many Sides? From an article in Mathematics Teaching 210 by Paul Stephenson
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 20 15 How many sides has the polygon?
How Many Sides? A polygon with ? sides (often called an n-gon)
How Many Sides? the external angle =360 ? ?
How Many Sides? first diagonal 1 2? ?
How Many Sides? ? ? 2?
How Many Sides? second diagonal ? 2? ?
How Many Sides? ? 2? 3?
How Many Sides? third diagonal 3 2? 3 2? 3?
How Many Sides? ? 4? 3?
How Many Sides? 2? fourth diagonal 2? 4?
How Many Sides? ? 5? 4?
How Many Sides? 5 2? fifth diagonal 5 2? 5?
How Many Sides? 5 2? These angles differ by 1 step, i.e. half the external angle. 2? each 2? So determine the external angle, ?, then determine the number of sides of the n-gon using: 3 2? ? =360 ? ? 1 2? Note that all the angles marked equal ? ? 2 .
Note to Teacher The difference between the angles shown is equal to half the external angle 360 So 2 ??????????=number of sides E.g. if the angles are 16 and 12 Then the difference is 4 So number of sides = 360 2 4 = 45
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 16 12 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 20 15 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 24 18 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 36 27 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 30 20 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 48 36 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 45 30 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 54 36 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 28 24 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 35 30 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 42 36 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 45 36 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 50 40 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 72 60 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 75 60 How many sides has the polygon? SIC_47
How Many Sides? (Not to scale) The diagram shows part of a regular polygon and part of some diagonals of the polygon drawn from one vertex. Two angles are marked. 72 54 How many sides has the polygon? SIC_47
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