What measuring method involves observing multiple direct and reversed angles?

The method that involves observing multiple direct and reversed angles is known as repetition. This technique is often used in surveying to improve the accuracy of angle measurements. By measuring an angle multiple times in both the direct and reverse directions, any systematic errors, such as those introduced by equipment or environmental conditions, can be identified and minimized.

Repetition contributes to a more reliable average measurement, as the repeated observations allow the surveyor to account for any discrepancies caused by factors like instrumental error or atmospheric refraction. By taking several measurements, surveyors can enhance the precision of their results, which is critical for accurate positioning and mapping in surveying projects.

Other options like triangulation, parallel measuring, and surveyal interpolation serve different purposes in the field of surveying and do not involve the specific process of observing angles repeatedly in both directions.