Sphinx
The Sphinx was a creature with a head and chest of a woman, body and legs of lion and wings of an eagle. The Sphinx was an offspring of Echidna and either Orthus or Typhon.
The Sphinx lived on the road west of Thebes. It was custom of the Sphinx to tell the riddle to travelling heading towards Thebes. If the traveller answers the riddle correctly, the traveller would be allowed to pass her. Giving the wrong answer, the Sphinx would kill and devour the traveller.
When Creon became regent at the death of King Laius, he offered the kingdom of Thebes and his beautiful sister, Jocasta (newly widowed) in marriage. When Oedipus correctly answered the riddle, the Sphinx killed itself by jumping off the cliff.
Oedipus became king, and unwittingly married his mother (Jocasta) and became father of their children.
See the House of Thebes for the entire tale of Oedipus.
In Egyptian mythology, the Sphinx appeared to be wingless