"Yo tengo un problema con la secretaria."
Translation:I have a problem with the secretary.
Perhaps. Or is it that her typing, spelling and grammar are atrocious! =D
"Problema" is a masculine noun, despite ending on an "a". There are a few exceptions to that rule, and you'll just have to learn them as you go.
It's because "problema" is a word taken from Greek. This shows up with many other words such as "dilemma" and "sistema," both being masculine. Happens in Italian too.
un tema, un problema, un planeta, un diá all have Greek origins. Therefore, most break the rule
Día doesn't derive from Greek (that would sound more like "emera" and it would be feminine), but it's a Latin origin, from the masculine "diēs", which got vulgarised to "*dia" while keeping its gender.
Why should it be "una"? Una is used for feminine nouns, whereas "problema" is definitely masculine noun, therefore it uses "un".
Why do you say the use of "the" is "another correct answer"?
What is the other correct answer?
I don't see how there could be any other than the one shown at the top of the page.
I understand that "problema" is a masculine noun from reading the other comments and replies, but is there a way to tell between masculine and feminine words when they don't follow the usual rule? Or are they just exceptions you have to get used to?
There are some patterns, but for some other words you can only memorise. Those original Greek-neutral nouns almost all end on '-ma': problema, dilema, tema, drama, programa, and so on. Then you have the job names ending on '-ta' which you can use for either gender: el/la artista, arquitecta, optimista, poeta, fundamentalista, et cetera. And there are those more-or-less one-ofs, like "el mapa", "el avión", and "la mano".