Which of the following tools can read horizontal and vertical angles electronically?

The correct choice of a theodolite is significant because this tool is specifically designed for measuring both horizontal and vertical angles with high precision. A theodolite typically features a telescope mounted on a rotating base, allowing it to swivel both horizontally and vertically. This dual capability is essential for various applications in surveying and construction, such as establishing control points, measuring distances indirectly, and aligning structures.

The theodolite's electronic variants, often called electronic theodolites, enhance measurement accuracy and convenience by displaying readings digitally, facilitating quick and precise angle assessments. This is especially important in professional settings where meticulous angle measurement is crucial for structural integrity and compliance with design specifications.

In contrast, other tools mentioned—like the transit and surveying compass—do not offer the same level of electronic measurement capability for both angles. While the clinometer is used for measuring inclined angles, it does not have the functionality for horizontal angles. Hence, the theodolite stands out as the appropriate tool for the task specified in the question.