Complex `[ML_(5)]` can exhibit trigonal bipyramidal and square pyramidal geometry. Determine total number of `180^@, 90^@ & 120^@` L-M-L bond angles.

Explanation

To determine the total number of `180^@`, `90^@`, and `120^@` L-M-L bond angles in the complex `[ML_(5)]` exhibiting trigonal bipyramidal and square pyramidal geometries, we will analyze each geometry step by step.

### Step 1: Analyze the Trigonal Bipyramidal Geometry

In the trigonal bipyramidal geometry, we have:
- 3 ligands in a plane forming a triangle (equatorial positions).
- 2 ligands above and below this plane (axial positions).

#### 180° Angles:
- There is **1 angle** between the two axial ligands (above and below the plane).
- Total = **1 (180° angle)**.

#### 120° Angles:
- The three equatorial ligands are spaced equally around the central metal, forming angles of 120° between them.
- Total = **3 (120° angles)**.

#### 90° Angles:
- Each axial ligand (above and below the plane) forms a 90° angle with each of the three equatorial ligands.
- Each axial ligand contributes 3 angles (one with each equatorial ligand).
- Total = **3 (from the upper axial ligand) + 3 (from the lower axial ligand) = 6 (90° angles)**.

### Summary for Trigonal Bipyramidal:
- 180° angles: 1
- 120° angles: 3
- 90° angles: 6

### Step 2: Analyze the Square Pyramidal Geometry

In the square pyramidal geometry, we have:
- 4 ligands forming a square base (equatorial positions).
- 1 ligand above the square base (axial position).

#### 180° Angles:
- There are **2 angles** formed by the diagonals of the square (between opposite ligands).
- Total = **2 (180° angles)**.

#### 120° Angles:
- There are **0 angles** of 120° in this geometry since the angles between the square ligands are 90°.

#### 90° Angles:
- The four ligands in the square base form **4 angles** of 90° with each other.
- The axial ligand above the square also forms **4 angles** of 90° with each of the four ligands in the square base.
- Total = **4 (from the square base) + 4 (from the axial ligand) = 8 (90° angles)**.

### Summary for Square Pyramidal:
- 180° angles: 2
- 120° angles: 0
- 90° angles: 8

### Step 3: Combine the Results

Now, we will combine the results from both geometries:

#### Total Count:
- **180° angles**: 1 (from trigonal bipyramidal) + 2 (from square pyramidal) = **3**
- **120° angles**: 3 (from trigonal bipyramidal) + 0 (from square pyramidal) = **3**
- **90° angles**: 6 (from trigonal bipyramidal) + 8 (from square pyramidal) = **14**

### Final Answer:
- Total number of bond angles:
- 180° angles: **3**
- 120° angles: **3**
- 90° angles: **14**