If `triangleABC and triangleDEF` are similar triangles such that `angleA =45^@ and angleF =56^@,` then find angle C

Answer

To solve the problem, we need to find angle C in triangle ABC given that triangle ABC is similar to triangle DEF, with angle A = 45° and angle F = 56°.

### Step-by-step solution:

1. **Understanding Similar Triangles**:
Since triangle ABC is similar to triangle DEF, we know that corresponding angles are equal. This means:
- Angle A (triangle ABC) = Angle D (triangle DEF)
- Angle B (triangle ABC) = Angle E (triangle DEF)
- Angle C (triangle ABC) = Angle F (triangle DEF)

2. **Given Angles**:
We are given:
- Angle A = 45°
- Angle F = 56°

3. **Finding Angle C**:
From the property of similar triangles, we have:
- Angle C = Angle F
Therefore, we can substitute the value of angle F:
- Angle C = 56°

4. **Conclusion**:
Thus, the measure of angle C in triangle ABC is 56°.

### Final Answer:
Angle C = 56°

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