The monomer of the polymer
`~CH_(2)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-CH_(2)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C)~`

Options

A.
B.
C.
D.

Explanation

To determine the monomer of the given polymer, we will analyze the structure of the polymer and identify the repeating units that make it up.

### Step-by-Step Solution:

1. **Identify the Structure of the Polymer:**
The polymer is represented as:
```
~CH2-CH(CH3)-C-CH2-CH(CH3)-C~
```
Here, we can see that the polymer consists of repeating units involving carbon (C) and hydrogen (H) atoms, with some branches of methyl (CH3) groups.

2. **Determine the Repeating Unit:**
From the structure, we can see that the repeating unit consists of:
- A carbon chain with two CH2 groups.
- Two CH groups that are each bonded to a CH3 group.
This suggests that the monomer has a double bond that allows for polymerization.

3. **Construct the Monomer:**
The monomer must have a structure that can repeat to form the polymer. Therefore, we can deduce that the monomer has:
- A double bond between two carbon atoms.
- Two CH3 groups attached to one of the carbon atoms.

The structure of the monomer can be represented as:
```
CH2=C(CH3)C(CH3)H
```
This indicates that the monomer has a double bond between the first two carbon atoms and branches of CH3 attached to the central carbon.

4. **Final Representation of the Monomer:**
The final representation of the monomer is:
```
CH2=C(CH3)C(CH3)H
```
This structure can polymerize to form the given polymer.

### Conclusion:
The monomer of the polymer is:
```
CH2=C(CH3)C(CH3)H
```