Calculate value of `(X+Y+Z)/(10)`, here X is O-N-O bond angle in `NO_(3)^(-)` Y is O-N-O bond angle in `NO_(2)^(+)` and Z is F-Xe-F adjacent bond angle in `XeF_(4)`.

Explanation

To solve the problem, we need to calculate the values of X, Y, and Z based on the given chemical species and their bond angles. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate X (O-N-O bond angle in NO₃⁻)
1. **Identify the structure of NO₃⁻**: The nitrate ion has a nitrogen atom bonded to three oxygen atoms.
2. **Determine the hybridization**:
- Valence electrons of nitrogen = 5
- Number of single bonds = 2 (two N-O single bonds)
- Cationic charge = 0 (since it’s an anion, we add 1)
- Hybridization formula:
\[ \text{Hybridization} = \frac{1}{2} \left( \text{Valence Electrons} + \text{Single Bonds} - \text{Cationic Charge} \right) = \frac{1}{2} (5 + 2 + 1) = 4 \]
- Hybridization of 4 corresponds to sp² (trigonal planar).
3. **Bond angle**: In a trigonal planar arrangement, the bond angles are 120°.
- Therefore, **X = 120°**.

### Step 2: Calculate Y (O-N-O bond angle in NO₂⁺)
1. **Identify the structure of NO₂⁺**: The nitronium ion has a nitrogen atom bonded to two oxygen atoms.
2. **Determine the hybridization**:
- Valence electrons of nitrogen = 5
- Number of single bonds = 0 (since both bonds are double bonds)
- Cationic charge = 1 (subtract 1)
- Hybridization formula:
\[ \text{Hybridization} = \frac{1}{2} (5 + 0 - 1) = 2 \]
- Hybridization of 2 corresponds to sp (linear).
3. **Bond angle**: In a linear arrangement, the bond angle is 180°.
- Therefore, **Y = 180°**.

### Step 3: Calculate Z (F-Xe-F bond angle in XeF₄)
1. **Identify the structure of XeF₄**: Xenon tetrafluoride has a xenon atom bonded to four fluorine atoms.
2. **Determine the hybridization**:
- Valence electrons of xenon = 8
- Number of single bonds = 4 (four Xe-F bonds)
- Cationic charge = 0
- Hybridization formula:
\[ \text{Hybridization} = \frac{1}{2} (8 + 4 + 0) = 6 \]
- Hybridization of 6 corresponds to sp³d² (octahedral).
3. **Bond angle**: In a square planar arrangement (due to lone pairs), the bond angle between adjacent fluorine atoms is 90°.
- Therefore, **Z = 90°**.

### Step 4: Calculate (X + Y + Z) / 10
1. **Sum the angles**:
\[ X + Y + Z = 120° + 180° + 90° = 390° \]
2. **Divide by 10**:
\[ \frac{X + Y + Z}{10} = \frac{390}{10} = 39 \]

### Final Answer:
The value of \((X + Y + Z) / 10\) is **39**.