If `DeltaABCis similar DeltaDEF`, such that `angleA = 47^(@)` and `angleE = 83^(@)`, then what is the value of `angleC` ?

Answer

To find the value of angle C in triangle ABC, given that triangle ABC is similar to triangle DEF, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of similar triangles**: Since triangle ABC is similar to triangle DEF, the corresponding angles are equal. This means:
- Angle A = Angle D
- Angle B = Angle E
- Angle C = Angle F

2. **Identify the given angles**: From the problem, we know:
- Angle A = 47°
- Angle E = 83°

3. **Find angle B**: Since angle B corresponds to angle E, we have:
- Angle B = Angle E = 83°

4. **Use the triangle angle sum property**: The sum of the angles in any triangle is always 180°. Therefore, we can write the equation for triangle ABC:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]

5. **Substitute the known values**: Plugging in the values we have:
\[ 47° + 83° + \text{Angle C} = 180° \]

6. **Combine the angles**: Add the angles A and B:
\[ 130° + \text{Angle C} = 180° \]

7. **Isolate angle C**: To find angle C, subtract 130° from both sides:
\[ \text{Angle C} = 180° - 130° \]

8. **Calculate angle C**:
\[ \text{Angle C} = 50° \]

### Final Answer:
Angle C = 50°

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