The image shows several triangles with numbers on two sides, with one missing number on the third side that needs to be determined. Let me analyze each triangle step by step and solve the missing values.

1. First Triangle:

• Numbers: 15 (top), 51 (bottom right), ? (bottom left).

We need to determine the pattern. Let's check the possible relationships.

• There seems to be a multiplication or addition pattern that might be consistent across the triangles.

2. Second Triangle:

• Numbers: 9 (top), 21 (bottom right), ? (bottom left).

3. Third Triangle:

• Numbers: 60 (top), 60 (bottom right), ? (bottom left).

4. Fourth Triangle:

• Numbers: 18 (top), 30 (bottom right), ? (bottom left).

5. Fifth Triangle:

• Numbers: 12 (top), 38 (bottom right), ? (bottom left).

Let me work on identifying the relationships between the numbers. I'll calculate the missing values.Based on the sum pattern (top + bottom right), the missing values in the triangles are as follows:

1. First Triangle: $15 + 51 = 66$
2. Second Triangle: $9 + 21 = 30$
3. Third Triangle: $60 + 60 = 120$
4. Fourth Triangle: $18 + 30 = 48$
5. Fifth Triangle: $12 + 38 = 50$

Thus, the missing values for each triangle (bottom left) are:

• First Triangle: 66
• Second Triangle: 30
• Third Triangle: 120
• Fourth Triangle: 48
• Fifth Triangle: 50

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:

1. Can you identify other patterns that could explain these numbers?
2. How would the pattern change if the operations used were multiplication or division?
3. What are some other common number patterns in similar puzzles?
4. Can you think of any real-life applications of number patterns like this?
5. How might this problem change if decimals or negative numbers were introduced?

Tip: Always check for simple arithmetic operations (addition, subtraction, multiplication) first when solving number pattern problems.