"Lustig," "Traurig," "Fertig," and "Wichtig"
Why do "lustig," "traurig," "fertig," and "wichtig" all end in 'ig'?
A lot of adjectives actually end with -ig. Words like "dreckig", "eilig", "giftig", "saftig" all end wit -ig. It is just a suffix for that makes adjectives out of nouns (example: "saft" means juice, add -ig and it becomes "juicy". The pronunciation of the suffix is different in many parts of the German speaking world. Germans would say "saftiCH" but Austrians and the Swiss would stick with the "g" sound.
I'm not sure. Maybe that's just how the language evolved. Every language has words that rhyme, and have the same endings. There does not have to be a reason as to why words end the way they do. That's like asking why does "dig, wig, and big" end in "ig"? Do you know the answer? You could always do more research into it. Sorry, I could not be of more help.
you can form an adjective out of a noun by adding an "-ig"., some examples: Lust - lustig, Hast - hastig, Fett - fettig, (sometimes losing the ending of the noun): Ecke - eckig, Trauer - traurig, (sometimes modifying the whole word): Schlaf - schläfrig, Eifer - eifrig.
But there are also a lot of adjectives ending in "-lich": Ende - endlich, Deut - deutlich, Haus - häuslich.
And, finally, there are words that end in "-ig" without being an adjective, f.e. Honig.