If `DeltaABC `is similar to `DeltaDEF`, such that `/_A = 47^@` and `/_E = 63^@` then `/_C` is equal to :

Options

A. A)`40^@`
B. B)`70^@`
C. C)`65^@`
D. D)`37^@`

Answer

To find the measure 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 triangles ABC and DEF are similar, their corresponding angles are equal. This means:
- Angle A corresponds to Angle D
- Angle B corresponds to Angle E
- Angle C corresponds to Angle F

2. **Identify the given angles**: We are given:
- Angle A = 47°
- Angle E = 63°

3. **Determine the corresponding angles**: From the similarity of the triangles:
- Angle D = Angle A = 47°
- Angle B = Angle E = 63°

4. **Use the triangle angle sum property**: The sum of the angles in any triangle is always 180°. Therefore, for triangle ABC:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
Substituting the known values:
\[ 47° + 63° + \text{Angle C} = 180° \]

5. **Calculate the sum of angles A and B**:
\[ 47° + 63° = 110° \]
So, we have:
\[ 110° + \text{Angle C} = 180° \]

6. **Solve for Angle C**:
\[ \text{Angle C} = 180° - 110° = 70° \]

Thus, the measure of angle C is **70°**.