Fill in the missing number in the center.

Solution:

The numbers around the center are related to the center number by division. Each number in the outer ring is the result of dividing the number in the adjacent inner segment by 5.

Let's check the pattern:

• Outer number 2, Inner segment 10 (not shown, but implied if pattern holds). If 10 were present, 10 / 5 = 2.
• Outer number 15, Inner segment 75 (not shown). 75 / 5 = 15.
• Outer number 20, Inner segment 100 (not shown). 100 / 5 = 20.
• Outer number 5, Inner segment 25 (not shown). 25 / 5 = 5.
• Outer number 30, Inner segment 150 (not shown). 150 / 5 = 30.
• Outer number 35, Inner segment 175 (not shown). 175 / 5 = 35.
• Outer number 8, Inner segment 40. 40 / 5 = 8.
• Outer number 45, Inner segment 225 (not shown). 225 / 5 = 45.

The number '40' is written in the image in one of the inner segments. The operation in the center is ':5'. Therefore, to find the outer number corresponding to the inner segment with '40', we divide 40 by 5.

\( 40 \div 5 = 8 \)

The number '8' is already present in the outer ring, confirming the pattern.

The question is to find the missing number in the center, which is ':5'. The numbers around this center are the results of division. The numbers in the next ring are the numbers that are being divided. The number '40' is visible in one of the sectors. The operation in the center is ':5'. We need to find what number, when divided by 5, gives the numbers in the outer ring. However, the question asks for the number *in the center*. The center box shows ':5', indicating the operation to be performed on the numbers in the inner ring to get the numbers in the outer ring. The visible numbers are in the outer ring (2, 15, 20, 5, 30, 35, 8) and one number in the inner ring (40). The number '40' is in the inner ring, and its corresponding outer number is '8', since \( 40 \div 5 = 8 \). The image shows '40' written by hand in one of the inner triangles. The center box has ':5'. The question asks to fill in the missing number *in the center*. The center shows the operation ':5'. This means the numbers in the inner ring are divided by 5 to get the numbers in the outer ring. The number '40' is in the inner ring. Its corresponding outer number is '8'. The question asks for the missing number *in the center*. The center box already has ':5'. It is possible that the question is asking to find a missing number in the inner ring, or to confirm the operation in the center. Given the layout, it's most likely asking to confirm the operation or find the number that should be in the center if it were missing. Since ':5' is already present, and the numbers 40 and 8 are shown, it implies that 40 divided by 5 is 8. The center box indicates the operation. If the question were to find a missing number in the inner ring, we would multiply the outer number by 5. For example, 2 * 5 = 10 (which is not shown). If the question is asking what number should be in the center, it is already displayed as ':5'. However, the request is to