If `Delta ABC ~ Delta DEF,` such that `angle A = 47 ^(@) and angle E = 83 ^(@),` what is the value of `angle C` ?

Options

A. `43 ^(@)`
B. `50^(@)`
C. `17^(@)`
D. `55^(@)`

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

### Step 2: Write down the known angles
From the problem, we know:
- Angle A = 47°
- Angle E = 83°

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

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

Substituting the known values:
\[ 47° + 83° + \text{Angle C} = 180° \]

### Step 5: Simplify the equation
Now, we can add the angles A and B:
\[ 47° + 83° = 130° \]
So, the equation becomes:
\[ 130° + \text{Angle C} = 180° \]

### Step 6: Solve for Angle C
To find angle C, we subtract 130° from both sides:
\[ \text{Angle C} = 180° - 130° \]
\[ \text{Angle C} = 50° \]

### Conclusion
The value of angle C is 50°.

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