Mark independent sides to be the measure of each of the variables. You can read off values using 3 particular directions that remain in that orientation as you move the point in the center. It makes it easier to locate and identify the internal points. For example. Label the triangle points to be 0. Label the sides in a clockwise direction to be 18, 36, 54, ... 180. Each point in the diagram defines the angles of unique triangle ABC that are easily read from the marked scales on each side..
One application is examining the composition of crystallizing magma, where every corner of the diagram represents one chemical component. Generally examining the behaviour of multi-component systems (even more than three compenents by adding cotectic lines and isotherms). You trace the crystallizing path along the diagram.
You may have some interest in a series of videos focused on reading crystallization paths: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-NuvEzQX0xnk.html