The question requires us to compare the bond angles in NH3 and CH4 molecules and then justify this comparison by choosing one of the available options.
First, let's remember the geometry of both NH3 and CH4 molecules. NH3 is a trigonal pyramidal molecule because N is bonded to 3 H and presents one lone pair of electrons, while CH4 presents a tetrahedral geometry (C in CH4 is bonded to 4 H atoms and doesn't present a lone pair).
Comparing the standard bond angles for both geometries, we would have 109.5°, however the bond angle for NH3 is smaller, at 107°. With that information, we can now remove options a, c and d.
Now, let's analyze the remaining options.
Option b actually presents a true information, however it doesn't explain the bond angle.
Option f: both N and C are sp3 hybridizated in NH3 and CH4, respectively.
Option g presents a wrong explanation because the bond angles in trigonal planar structures are actually greater than tetrahedral structures (120° x 109.5°).
Therefore, letter E would be the best option, since it presents a true information that is related to the bond angles (the lone pair of electrons in N does present a repulsive force to the bonded electrons).