Which equipment helps in measuring horizontal and vertical angles?

The equipment that helps in measuring horizontal and vertical angles is the transit and theodolite. These instruments are specialized tools used in surveying and construction to provide precise measurements of angles in both the horizontal and vertical planes.

A transit is typically used to take angular measurements in a horizontal plane and is equipped with a sighting telescope for accurate targeting. A theodolite enhances this functionality by allowing for the measurement of vertical angles as well, making it an essential tool for geodetic surveys, construction projects, and other applications where precise angle measurements are necessary.

In contrast to the other options, the transit and theodolite are specifically designed for this purpose. The analog inclusion data system, while useful for other types of data processing, does not directly measure angles. The horizontal plane reference is more about ensuring level alignment rather than measuring angles. Alignment sights might help with directional aiming but do not provide the detailed angle measurements that a transit or theodolite would. Thus, the transit and theodolite are the go-to choices for accurate angular measurement in both dimensions.