The correct answer is option 'C', which states that balancing methods can be applied only when the survey forms a closed polygon traverse.

Explanation:
Balancing methods in surveying are used to adjust the measured angles and distances to ensure that the traverse is closed and accurate. These methods are employed to minimize the errors and discrepancies that may arise during the surveying process.

A closed polygon traverse refers to a survey where the starting point and the ending point are the same, and all the lines form a closed shape. This type of traverse is essential for applying balancing methods because it allows for the calculation and adjustment of the errors in the survey.

Here are the reasons why balancing methods can be applied only when the survey forms a closed polygon traverse:

1. Error detection: A closed polygon traverse enables the surveyor to identify errors in the measurements. By comparing the sum of the included angles with the expected value (360 degrees for a closed polygon), any discrepancies or mistakes can be detected.

2. Error distribution: Balancing methods distribute the errors proportionately among the measured angles and distances in the traverse. This distribution is based on the principle of least squares, which aims to minimize the overall error in the survey. However, this distribution can only be done accurately when the traverse is closed and forms a polygon.

3. Adjustment computation: Balancing methods involve computing the adjustments required to close the traverse accurately. These adjustments are calculated based on the errors detected and the distribution of these errors among the traverse measurements. To perform these calculations, a closed polygon traverse is necessary.

4. Error correction: Once the adjustments are computed, they can be applied to the measured angles and distances to correct the errors. This correction process ensures that the traverse closes accurately, and the measurements are adjusted to their true values. However, this correction can only be done effectively when the traverse is closed and forms a polygon.

In summary, balancing methods in surveying can only be applied when the survey forms a closed polygon traverse. This type of traverse allows for error detection, error distribution, adjustment computation, and error correction, which are the fundamental steps in balancing a survey. Without a closed polygon traverse, these methods cannot be accurately and effectively applied.