Angosia III was a class M planet, homeworld of the Angosians. In 2366, the Angosian government petitioned for membership in the Federation, and the USS Enterprise-D was dispatched to conduct a follow-up visit. During this visit, it was learned that the Angosian government unduly held Tarsian War veterans as prisoners on one of Angosia's moons, Lunar V. Federation membership was postponed. (TNG: "The Hunted")
From the designation, it suggests that Angosia III has at least five moons.