This is an analogy question. We need to find the relationship between 72 and 90 and apply the same logic to 156 to find the missing number.

Step 1: Analyze the Relationship between 72 and 90

Let's examine the difference and the ratio between 72 and 90:

• Difference: 90 - 72 = 18
• Ratio: 90/72 = 1.25 or 5/4

Neither a simple difference nor a simple ratio seems to directly relate 72 to 90. Let's explore other possibilities.

Step 2: Consider Other Relationships

Let's look at the prime factorization:

• 72 = 8 x 9 = 2³ x 3²
• 90 = 9 x 10 = 2 x 3² x 5

The relationship isn't immediately obvious through prime factorization either.

Step 3: Try Different Arithmetic Operations

Let's try adding a number to 72 to get 90. If we add 18, we get 90. Let's see if adding 18 to 156 works.

156 + 18 = 174

This doesn't match any of the options.

Step 4: Let's Explore Another Pattern

Let's consider the pattern of adding increasing multiples of 18:

• 72 + 18 = 90 (1 x 18)

Now, let's apply this to 156. Note that this pattern seems promising if we consider that it is possible there's an underlying pattern we haven't identified yet.

Let's try adding multiples of 18 to 156:

• 156 + 18 = 174
• 156 + 36 = 192

None of the options fit this pattern exactly.

Step 5: Consider a Different Approach

Let's look for a different mathematical relationship. It's worth noting that none of the simple arithmetic operations readily produce an answer. Sometimes, complex numerical relationships are present in these types of questions.

Let's re-examine 72 and 90. Notice that 90 is 1.25 times 72 (90/72 = 1.25). Let's apply this to 156.

156 * 1.25 = 195

This is not an option. It seems that we need to find another pattern.

Step 6: Final Analysis (A More Complex Pattern)

Let's try a more complex pattern. There doesn't seem to be a straightforward mathematical relationship. It's possible this question has an error or the logic is very obscure. There's a need to provide further clarity.

Conclusion: Without a clear and consistent pattern or logical relationship between the given numbers, it is difficult to definitively solve this question. The provided options do not appear to follow any easily discernible pattern.