Concept:
Bond angle is affected by electron pair repulsion. According to VSEPR theory, lone pair-bond pair repulsion is stronger than bond pair-bond pair repulsion.
Step 1: Bond angle in \(CH_4\).
Methane has tetrahedral geometry with bond angle:
\[
109.5^\circ
\]
Step 2: Bond angle in \(NH_3\).
Ammonia has one lone pair on nitrogen. Due to this lone pair, the bond angle decreases to about:
\[
107^\circ
\]
Step 3: Check Assertion.
Since \(107^\circ < 109.5^\circ\), the bond angle in \(NH_3\) is smaller than in \(CH_4\).
\[
A \text{ is correct}
\]
Step 4: Check Reason.
The lone pair in \(NH_3\) repels bonding pairs more strongly and compresses the bond angle.
\[
R \text{ is correct}
\]
Step 5: Check explanation.
The reason correctly explains why bond angle in \(NH_3\) is smaller than in \(CH_4\).
\[
\therefore \text{Correct Answer is (A)}
\]