We cannot construct a triangle, if we are given

Options

A. only three angles
B. two angles and one side
C. only three sides
D. two sides and included angle

Answer

To determine when we cannot construct a triangle based on given parameters, let's analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Options**:
We have four options to consider:
- Option A: 3 angles
- Option B: 2 angles and 1 side
- Option C: 3 sides
- Option D: 2 sides and the included angle

2. **Analyzing Option A (3 Angles)**:
- If we are given three angles, let's denote them as \( A, B, \) and \( C \).
- According to the triangle angle sum property, the sum of the angles in a triangle must equal \( 180^\circ \).
- However, knowing only the angles does not provide any information about the side lengths.
- Therefore, multiple triangles can be formed with the same angles but different side lengths (e.g., similar triangles).
- **Conclusion**: We cannot construct a specific triangle with just three angles.

3. **Analyzing Option B (2 Angles and 1 Side)**:
- If we have two angles and one side, we can use the known side as a base.
- The third angle can be calculated using the angle sum property: \( C = 180^\circ - (A + B) \).
- With this information, we can construct a unique triangle.
- **Conclusion**: A triangle can be constructed with 2 angles and 1 side.

4. **Analyzing Option C (3 Sides)**:
- If we are given three sides, we can use the triangle inequality theorem to check if a triangle can be formed.
- If the sides satisfy the triangle inequality, a unique triangle can be constructed.
- **Conclusion**: A triangle can be constructed with 3 sides.

5. **Analyzing Option D (2 Sides and the Included Angle)**:
- Given two sides and the included angle, we can apply the Law of Cosines or simply construct the triangle using the two sides and the angle between them.
- This will yield a unique triangle.
- **Conclusion**: A triangle can be constructed with 2 sides and the included angle.

### Final Conclusion:
Based on the analysis, the only option where we cannot construct a specific triangle is **Option A: 3 angles**.