"My boyfriend is very handsome."
Translation:Erkek arkadaşım çok yakışıklı.
Well, I think "erkek" has the meaning of "male" here. So here is a subtlety you have to know about:
Erkek arkadaş = boyfriend. (male friend)
Kız arkadaş = girlfriend. (girl friend).
Note that even though you say "erkek arkadaş" you don't say "kadın arkadaş". A "kız arkadaş" is always young, how cool! ;)