Step 1: Write reaction of \(F_2\) with dilute NaOH.
\[
2F_2 + 2NaOH \rightarrow 2NaF + OF_2 + H_2O
\]
So gaseous product \(A = OF_2\) (oxygen difluoride).
Step 2: Determine shape of \(OF_2\).
Central atom is oxygen.
O has 2 bond pairs and 2 lone pairs \(\Rightarrow\) bent structure like \(H_2O\).
Step 3: Compare bond angle.
Bond angle in \(H_2O\) is \(104.5^\circ\).
In \(OF_2\), fluorine is more electronegative, pulling bonding pairs away, reducing repulsion.
So bond angle is less than water: around \(103^\circ\).
Final Answer:
\[
\boxed{103^\circ}
\]