What is the molecular geometry of Br$_3$ $^-$?

In order to determine the geometry of Br$_3$$^-$, first, we need to draw its Lewis dot structure.

First, let's determine the number of valence electrons in Br$_3$$^{-}$. Bromine is a member of group 7A so it has 7 valence electrons. Don't forget to add up one electron because of the 1- charge:

$$3 \times 7 + 1 =22~\text{valence e}^-$$

Now, the first step in drawing Lewis structures is connecting all the atoms with a single bond:

We used 4 electrons so we have 18 electrons left.