The angular houses are also the four most consequential compartments of the house catalogue, and reading their subjects together shows why the tradition treated the group as a unit.
The first is the native: the body, the life, the stature, the character. The fourth is the ground: the parents, the land, the home, the end of the matter, and what lies under a life. The seventh is the other party: the spouse, the partner, the opponent. The tenth is the standing: office, honour, trade, reputation and, in Lilly, the mother. Between them they cover a person, their origin, their significant other and their public position, which is close to a complete account of a life at the scale a chart is asked about.
Two of the four form the axis of the horizon and two the axis of the meridian, and the tradition reads them as different questions. The horizon axis, first and seventh, is the self and the other. The meridian axis, fourth and tenth, is the private ground and the public position. Modern astrology usually calls the second the parental axis and argues about which parent belongs at which end, a dispute recorded elsewhere in this atlas.
A planet on an angle in a chart with an accurate birth time is the strongest single testimony most readings have. The qualification matters. The angles move about a degree every four minutes of clock time, so an angular placement is the part of a chart most sensitive to a wrong birth time, and the tradition developed rectification methods for exactly that reason.
Sources The Daimon in Hellenistic Astrology: Origins and InfluenceDorian Gieseler Greenbaum with Christian AstrologyWilliam Lilly