1. Let's analyze the pattern in the given triangles one by one. 2. Each triangle has a top number and two bottom numbers side-by-side. 3. Try to find the relation between the top number and the two bottom numbers for the known triangles. 4. For the first triangle: top = 5, bottom left = 20, bottom right = 10. 5. Notice that $20 + 10 = 30$, which is $5 \times 6$. 6. For the second triangle: top = 3, bottom left = 4, bottom right = 14. 7. $4 + 14 = 18$ and $3 \times 6 = 18$. 8. For the third triangle: top = 11, bottom left = 48, bottom right = 18. 9. $48 + 18 = 66$ and $11 \times 6 = 66$. 10. We see the pattern: sum of bottom numbers = top number $\times 6$. 11. Use this pattern for the triangle with missing bottom left number and top = 15, bottom right = 51. 12. Calculate the sum: $15 \times 6 = 90$. 13. Missing bottom left $= 90 - 51 = 39$. 14. The options for this missing number are: A. 60 B. 72 C. 84 D. 39 E. 66. 15. Option D (39) matches. 16. For the next triangle: top = 9, bottom left = 21, bottom right unknown. 17. Calculate sum: $9 \times 6 = 54$. 18. Missing bottom right $= 54 - 21 = 33$. 19. Options: A. 47 B. 33 C. 62 D. 30 E. 12. 20. Option B (33) matches. 21. Triangle with unknown top, bottom left = 60, bottom right = 60. 22. Sum of bottom numbers $= 60 + 60 = 120$. 23. Top number $= 120 / 6 = 20$. 24. Options: A. 30 B. 180 C. 120 D. 60 E. 20. 25. Option E (20) matches. 26. Triangle with unknown top, bottom left = 18, bottom right = 30. 27. Sum = $18 + 30 = 48$. 28. Top number = $48 / 6 = 8$. 29. Options: A. 48 B. 24 C. 8 D. 64 E. 12. 30. Option C (8) matches. 31. Triangle with top = 12, missing bottom left, bottom right = 38. 32. Sum = $12 \times 6 = 72$. 33. Missing bottom left = $72 - 38 = 34$. 34. Options: A. 76 B. 34 C. 50 D. 68 E. 64. 35. Option B (34) matches. Final answers: - Triangle with 15 at top: missing bottom left = 39 (D). - Triangle with 9 at top: missing bottom right = 33 (B). - Triangle with missing top, bottom numbers 60 and 60: top = 20 (E). - Triangle with missing top, bottom 18 and 30: top = 8 (C). - Triangle with top 12, missing bottom left, bottom right 38: missing bottom left = 34 (B).