Step 1: Understand the question.
We must find the O-S-O bond angle in the $\text{SO}_2$ molecule. We use VSEPR theory, which predicts shape from electron pairs around the central atom.
Step 2: Count groups around sulfur.
Sulfur is the central atom. It forms bonds with two oxygen atoms and also keeps one lone pair of its own. So it has 2 bonding regions plus 1 lone pair, giving a steric number of 3.
Step 3: Find the hybridisation.
A steric number of 3 means $sp^2$ hybridisation.
Step 4: Find the ideal angle.
A perfect $sp^2$ shape is trigonal planar with angles of $120^\circ$.
Step 5: Adjust for the lone pair.
A lone pair pushes harder than bonding pairs, so it squeezes the two S=O bonds a little closer. This bends the molecule and lowers the angle slightly below $120^\circ$, to about $119.5^\circ$.
Step 6: Pick the answer.
The O-S-O angle is about $119.5^\circ$, which is option 4.
\[ \boxed{119.5^\circ} \]