How many more diagonals are in an octagon than in a hexagon?

Source: NCCTM Mathematics Teacher

**SOLUTION**

**
**We draw a diagonal by connecting two non-adjacent vertices. For example, is a diagonal but and are not. How many ways can we choose two vertices from a set of eight vertices?

1. N 8. N 14. N 19. N 23. N 26. N 28. N

2. Y 9. Y 15. Y 20. Y 24. Y 27. Y

3. Y 10. Y 16. Y 21. Y 25. Y

4. Y 11. Y 17. Y 22. Y

5. Y 12. Y 18. Y

6. Y 13. Y

7. N

Number of diagonals in an octagon

How many ways can we choose two vertices from a set of six vertices of a hexagon?

1. N 6. N 10. N 13. N 15. N

2. Y 7. Y 11. Y 14. Y

3. Y 8. Y 12. Y

4. Y 9. Y

5. N

Number of diagonals in a hexagon

How many more diagonals are in an octagon than in a hexagon?

**Answer**: