The instrument used to measure horizontal, vertical angles, and planes is called a theodolite.
A theodolite is a precision optical instrument that consists of a telescope mounted on a base with graduated circles. It has a vertical axis and a horizontal axis that allow for precise measurements of angles in both the horizontal and vertical planes.
The telescope on the theodolite is used to sight a target, and then the angles can be read from the graduated circles. This allows surveyors to accurately measure angles and distances, which are crucial for creating maps, determining property boundaries, and conducting construction surveys.
Overall, a theodolite is an essential tool for surveyors, and its precise measurements help ensure that their work is accurate and reliable.