Sagittarius on the inside, Libra on the way in.
Your sun in Sagittarius (fire, mutable) is the engine — what burns at the centre, what adapts when you are at home in yourself. Your Libra rising (air, cardinal, ruled by Venus) is the door — the way you arrive in a room, the first read the world takes of you, the body you walk in.
Strangers tend to assume you are witty and detached — that is the Libra arriving first. Then they get to know you and discover the Sagittarius fire underneath, which can be a layered second read — they have to update their first impression.
Reads as Libra until you trust them; then Sagittarius comes through. The mutable-cardinal mix means you adapts on the inside while starts on the outside — internal and external rhythms are different, which is its own work.