How Many Sides?

Determine the number of sides of a polygon using angles and diagonals, as illustrated with diagrams. Learn the formula and steps to solve for the sides of an n-gon based on given angles.

• Mathematics
• Polygon
• Angles
• Diagonals
• Mathematics Teaching

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Uploaded on Feb 26, 2025 | 0 Views

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Presentation Transcript

1. How Many Sides? From an article in Mathematics Teaching 210 by Paul Stephenson

2. 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?

3. How Many Sides? A polygon with ? sides (often called an n-gon)

4. How Many Sides? the external angle =360 ? ?

5. How Many Sides? first diagonal 1 2? ?

6. How Many Sides? ? ? 2?

7. How Many Sides? second diagonal ? 2? ?

8. How Many Sides? ? 2? 3?

9. How Many Sides? third diagonal 3 2? 3 2? 3?

10. How Many Sides? ? 4? 3?

11. How Many Sides? 2? fourth diagonal 2? 4?

12. How Many Sides? ? 5? 4?

13. How Many Sides? 5 2? fifth diagonal 5 2? 5?

14. 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 .

16. 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

17. RESOURCES

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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