To determine which of the options is incorrect, we will analyze each statement one by one.
### Step-by-Step Solution:
1. **Statement A: "An angle of 52.5 degrees can be constructed."**
- This statement is true. Any angle can be constructed using a compass and a straightedge, including 52.5 degrees. Therefore, this option is not incorrect.
**Hint:** Remember that any angle can be constructed with the right tools.
2. **Statement B: "Triangle ABC can be constructed where AB = 5 cm, ∠A = 45°, and BC + AC = 5 cm."**
- Here, we need to check the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Given that BC + AC = 5 cm, and AB = 5 cm, we can see that:
- BC + AC must be greater than AB (5 cm).
- However, since BC + AC = 5 cm, it does not satisfy the triangle inequality (it must be greater than 5 cm).
- Therefore, this statement is incorrect.
**Hint:** Recall the triangle inequality theorem when checking the feasibility of constructing a triangle.
3. **Statement C: "Triangle ABC can be constructed where AB = 3 cm, ∠A = 30°, and BC + AC = 6 cm."**
- For this statement, we check the triangle inequality again:
- BC + AC > AB (3 cm).
- Since BC + AC = 6 cm, this is greater than 3 cm, satisfying the condition.
- Therefore, this statement is true.
**Hint:** Ensure that the sum of any two sides is greater than the third side.
4. **Statement D: "Triangle ABC can be constructed where AB = 4 cm, ∠A = 60°, and BC + AC = 8 cm."**
- Again, we apply the triangle inequality:
- BC + AC must be greater than AB (4 cm).
- Since BC + AC = 8 cm, this is greater than 4 cm, satisfying the condition.
- Therefore, this statement is true.
**Hint:** Always check if the sum of two sides is greater than the third side.
### Conclusion:
The incorrect option is **B**, as it violates the triangle inequality theorem.
