The reactivity of amines towards dilute \( \text{HCl} \) is governed by their basicity, which is influenced by factors such as electron-donating groups and steric hindrance.
Step 1: Analyze the basicity of different amines.
Methylamine (\( \text{CH}_3\text{NH}_2 \)) is a primary amine where the methyl group (\( \text{CH}_3 \)) donates electrons via an inductive effect, increasing the electron density on nitrogen. However, this effect is weaker compared to secondary amines, making methylamine less basic.
Dimethylamine (\( (\text{CH}_3)_2\text{NH} \)) is a secondary amine with two \( \text{CH}_3 \) groups. These groups provide a stronger electron-donating inductive effect, enhancing the electron density on nitrogen and making dimethylamine the most basic of the given options. The lower steric hindrance in dimethylamine compared to tertiary amines also contributes to its high reactivity towards dilute \( \text{HCl} \).
Trimethylamine (\( (\text{CH}_3)_3\text{N} \)) is a tertiary amine with three \( \text{CH}_3 \) groups. Although the inductive effect is strong, the increased steric hindrance around nitrogen reduces the availability of the lone pair for protonation, making trimethylamine less reactive than dimethylamine.
Aniline (\( \text{C}_6\text{H}_5\text{NH}_2 \)) is less basic than aliphatic amines because the lone pair on nitrogen is delocalized into the aromatic ring via resonance. This reduces the availability of the lone pair for protonation, making aniline the least reactive among the given options.
Step 2: Conclusion.
Dimethylamine, with its stronger electron-donating groups and lower steric hindrance, is the most reactive towards dilute \( \text{HCl} \).
\[
(\text{CH}_3)_2\text{NH} + \text{HCl} \to (\text{CH}_3)_2\text{NH}_2^+ + \text{Cl}^-.
\]
Final Answer:
\[
\boxed{(\text{CH}_3)_2\text{NH}}
\]