What angle measurement technique can be applied in both direct and inverted positions of an instrument?

The correct answer is founded in the understanding that doubling the angle is a technique that can be applied in both direct and inverted positions of a surveying instrument. This method involves measuring an angle from one position and then re-measuring the same angle from the opposite or inverted position to ensure accuracy and consistency in the data collected.

Doubling the angle is particularly useful because it reduces systematic errors that may arise due to the orientation of the instrument or environmental factors. By measuring the angle from both sides, surveyors can verify that measurements are precise and account for any discrepancies that may occur during positioning.

In contrast, techniques like bisecting the angle focus on finding the midpoint of an angle but don't necessarily account for variations between direct and inverted measurements. Quick setup angle and reversing the angle also pertain to various measurement methods, but they may not effectively validate measurements under both orientations of the instrument in the same manner that doubling the angle does. This makes doubling the angle the most reliable choice for ensuring accurate angle measurements in both positions.