Learn Italian: La sua vita in città è molto tranquilla.

Not exactly! In Italian, possessive adjectives like sua agree with the thing being owned, not the owner. La sua is feminine singular to match vita (life). So la sua vita could actually mean his life or her life depending on the context. Notice that you also need the definite article la before it!

The English translation says in the city. Why is there no word for the before città?

For certain common locations, Italian uses the preposition in without any definite article. Just like we say in town or in bed in English, Italians say in città (in the city), in banca (at the bank), and in classe (in class).

Since vita is a feminine noun, why didn't molto change to molta?

In this sentence, molto means very and is describing how quiet the life is. When molto acts as very, it never changes its ending. It only changes to match a noun when it means a lot of or many (such as molta acqua for a lot of water).

Why does tranquilla end in a?