Fake A Smile is written in the key of G Major.
According to the Theorytab database, it is the 3rd most popular key among Major keys and the 3rd most popular among all keys. Major keys, along with minor keys, are a common choice for popular songs. The three most important chords, built off the 1st, 4th and 5th scale degrees are all major chords (G Major, C Major, and D Major).
See the G Major Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!