A Vulcan statue perched at an odd angle
An angle was the distance between two intersecting lines when traveling circularly from one to the other. It was a central concept in the fields of mathematics, geometry, and trigonometry. It was measured using degrees (360 of which completing a full circle) and minutes.
In starship operation, headings were expressed in angles. (TNG: "Datalore")
According to T'Pol, a Vulcan icon of Surak at a shrine in the atrium of the monastery at P'Jem was perched at an odd angle. (ENT: "The Andorian Incident")
One variable in transporter operation was the angle of dispersion. In 2267, Captain James T. Kirk ordered the entity known as Redjac, inhabiting the body of Mr. Hengist, to be beamed out into deep space with the widest angle of dispersion possible. (TOS: "Wolf in the Fold")
Phasers could be set to a wide-angle setting, in which the phaser energy was distributed in a wide angle. (DS9: "The Way of the Warrior")