What technique involves determining the positions of survey points by measuring the angles of triangles?

The correct answer is triangulation. This technique involves the measurement of angles between known survey points, forming a triangle. By using the principles of geometry, specifically the Law of Sines and the Law of Cosines, surveyors can calculate the distances to unknown points based on the measured angles within the triangles.

Triangulation is particularly useful in land surveying and geodesy as it allows surveyors to establish the relative positions of points over large distances. By using a baseline (a known distance between two points) and measuring angles to other points, the positions of those points can be accurately determined without needing to directly measure distances to them.

In contrast, trilateration relies on measuring distances between points rather than angles, and is typically used in satellite navigation systems. Geodetic surveys involve broader principles of measuring large areas and may use triangulation among other methods, but it does not specifically refer to the angular measurement aspect. Plane table surveys use a different method for mapping and do not involve the triangulation technique described in the question.