In `DeltaXYZ, angleX=45^(@), angleY=75^(@)` in another triangle ABC, `angleA=45^(@), angleC=60^(@)` and AC = 6 cm. find XZ, given that `DeltaXYZ cong DeltaABC`.

Answer

To solve the problem, we need to find the length of side XZ in triangle XYZ, given that triangle XYZ is congruent to triangle ABC.

### Step-by-step Solution:

1. **Identify the Angles in Both Triangles**:
- In triangle XYZ:
- Angle X = 45°
- Angle Y = 75°
- Angle Z can be calculated as:
\[ \text{Angle Z} = 180° - \text{Angle X} - \text{Angle Y} = 180° - 45° - 75° = 60° \]
- In triangle ABC:
- Angle A = 45°
- Angle C = 60°
- Angle B can be calculated as:
\[ \text{Angle B} = 180° - \text{Angle A} - \text{Angle C} = 180° - 45° - 60° = 75° \]

2. **Establish the Congruence**:
- Since triangle XYZ is congruent to triangle ABC (∆XYZ ≅ ∆ABC), the corresponding angles and sides are equal.
- Therefore, we have:
- Angle X corresponds to Angle A
- Angle Y corresponds to Angle B
- Angle Z corresponds to Angle C

3. **Use Corresponding Parts of Congruent Triangles (CPCT)**:
- According to the properties of congruent triangles, the corresponding sides are equal.
- We know that AC = 6 cm in triangle ABC.
- Thus, by CPCT:
\[ XZ = AC \]
- Therefore:
\[ XZ = 6 \text{ cm} \]

4. **Final Answer**:
- The length of side XZ is 6 cm.

### Summary:
Thus, the length of XZ in triangle XYZ is **6 cm**.

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