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.
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")