To convert 123.60' into centesimal system, we need to first convert minutes to decimal degrees.
FORMULA:

STEPS:
- In this case, we have:

- We can now convert the decimal deg to centesimal degrees. Since a right angle is 100 centesimal degrees, we can this formula:

- In this case, we have:

Therefore, the angle 123.60' is approximately equal to 136.68 centesimal degrees.