The most appropriate synonym for "announce" is "advertise." "Announce" means to make something known or to declare publicly, and "advertise" involves making information or products known to the public through various means. The other options, such as "denounce" (to condemn publicly), "secret" (concealed), and "hide" (to keep something out of sight), have different meanings and do not convey the idea of making information widely known as "advertise" does.

The most appropriate synonym for "transient" is "temporary." Both words convey the idea of something lasting for a short duration or not permanent. The other options— "transform" (change), "transmit" (send), and "trap" (catch)— have different meanings and do not capture the sense of impermanence conveyed by "transient."