Understanding the Problem
To find the angles of the triangle, we start with the given information:
- One of the exterior angles is 120 degrees.
- The interior opposite angles are in the ratio 2:3.

Finding the Interior Angles
1. **Relation of Exterior and Interior Angles**:
- The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- Let the two opposite interior angles be \(2x\) and \(3x\) (since they are in the ratio 2:3).
2. **Setting Up the Equation**:
- According to the exterior angle theorem:
\[ 2x + 3x = 120 \]
3. **Solving for \(x\)**:
- Combine the terms:
\[ 5x = 120 \]
- Divide by 5:
\[ x = 24 \]
4. **Calculating the Angles**:
- Now substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 2x = 2 \times 24 = 48 \text{ degrees} \]
- Second angle:
\[ 3x = 3 \times 24 = 72 \text{ degrees} \]

Finding the Third Angle
1. **Using the Triangle Angle Sum Property**:
- The sum of all interior angles in a triangle is 180 degrees.
- Let the third angle be \(y\).
- Thus:
\[ 48 + 72 + y = 180 \]
2. **Solving for \(y\)**:
- Combine the known angles:
\[ 120 + y = 180 \]
- Subtract 120:
\[ y = 60 \text{ degrees} \]

Final Angles of the Triangle
- The angles of the triangle are:
- \(48\) degrees
- \(72\) degrees
- \(60\) degrees
This gives us a complete understanding of the triangle's angles based on the given exterior angle and the ratio of the interior opposite angles.