NH₃ is trigonal pyramidal because it has 4 electron domains, one of them being a lone pair of electrons and the other three being H atoms. When this is arranged in a three-dimensional space, it is trigonal pyramidal in shape.

CO2H is trigonal planar, so the bond angles will be 120 only. 

COH₂:        

               :O:

                ||

           H—C—H

This is a trigonal planar molecule, which only has bond angles of 120^o

has four bonding regions and no lone pairs, so it has a tetrahedral geometry. The bond angles between all of the bonded atoms is .

has three bonds and one lone pair, so it has a tetrahedral geometry with a trigonal pyramidal shape. Due to its shape, the bond angles are .

In a compound, the atoms (and electron lone pairs) will be as far away from each other as possible due to the repulsive forces between electrons.

Methane  will have a tetrahedral geometry with bond angles of 109.5^o. Both ammonia and water have lone electron pairs, which will decrease the bond angle between atoms. Water will be bent, while ammonia will be trigonal pyramidal. Bent and trigonal pyramidal are both permutations of tetrahedral, with slightly decreased bond angles.

 does not have lone electron pairs and will have a trigonal planar geometry. This results in bond angles of 120^o. As a result,  has the largest bond angles out of the options.

The carbon in the molecule is  hybridized and contains no lone pairs attached to it. This will give the molecule a tetrahedral geometry, standard of a central atom with four single bonds. Bond angles in a tetrahedral molecule are all .

has two bonding regions and no lone pairs around the central atom, so it has a linear geometry, so its bond angle is .

has four bonding regions and no lone pairs around the central atom, so it has a tetrahedral geometry with bond angles of .

has six bonding regions and no lone pairs around the central atom, so it has an octahedral geometry with bond angles of and . For the sake of ranking, we will only consider the smaller angle.

has three bonding regions and one lone pair around the central atom, so it has a trigonal pyramidal geometry with bond angles of .

has three bonding regions and no lone pairs around the central atom, so it has a trigonal planar geometry with bond angles of .

has four bonding regions and no lone pairs, so it has a tetrahedral geometry. has two bonding regions, but it also has two lone pairs, so it has a bent geometry.

According to hybrid orbital bonding theories, the hybridization state will use a number of orbitals equal to the steric number. The steric number is the number of atoms bonding to the central atom, plus any additional lone pairs.

Nitrogen (N) is the central atom because hydrogen atoms are never central. 

Nitrogen has 5 valence electrons, and in ,  it is bonded with 3 hydrogen atoms, which each borrow one of nitrogen's electrons to create a covalent bond. Subtracting those 3 borrowed electrons from its original 5 leaves 2 left, or 1 lone pair.

In total, the nitrogen atom has 3 bonds and 1 lone pair for a steric number of 4. As a result, its hybridization state must use 4 orbitals. The lowest energy way to do that is to use the lowest energy orbitals that are available. In this case, those are the s and p orbitals. So it uses one s and three p orbitals, giving the sp³ hybridization state.