The instrument used to measure angular distances between two objects is a sextant.

Here's why:

* Sextants are specifically designed for measuring angles, particularly between celestial objects (like stars and the horizon) for navigation.

* They use mirrors to reflect light from two objects, allowing the user to align them and read the angle on a calibrated scale.

While other instruments exist for angle measurements, the sextant is the most common and historically significant tool for measuring angular distances in astronomy and navigation.