To determine the largest bond angle, we could determine the molecular geometry of each species first.
`BCl_3` : Boron is connected to three chlorines through single bonds. Since boron only has three valence electrons, the three single bonds already account for them - no lone pair. Hence, the shape is trigonal planar with a bond angle of 120 degrees.
`NH_3` : Like boron trichloride, nitrogen is attached to the hydrogens through single bonds. However, nitrogen has 5 valence electrons and hence still has a lone pair (an additional electron domain). The shape of this molecule is trigonal pyramidal with bond angle of 107 degrees.
`BeCl_2` : Beryllium has two valence electrons, attached through single bonds to two chlorines. The shape is thus linear with bond angle of 180 degrees.
`H_2O` : Oxygen has six valence electrons. Two of these are used to form single bonds with the two hydrogens. Hence, there are still four electrons - these constitute two lone pairs. Hence, we have two bonded domains, and two electron pairs. Water is a bent molecule so the angle is 109.5 degrees.
Given these, we see that beryllium chloride has the largest angle at 180 degrees. Answer is C.