A person contributed his total salary of a month for three social welfare societis A, B and C. The ratio of total salary, share of A, and share of B is 20 : 5 : 8. Find the central angle of sector, which represents the share of C.

Options

A. `72 1^(@)/2`
B. `126^(@)`
C. `105^(@)`
D. `67 1^(@)/2`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Ratios
We are given the ratio of the total salary, share of A, and share of B as 20:5:8. This means:
- Total Salary = 20 parts
- Share of A = 5 parts
- Share of B = 8 parts

### Step 2: Calculate the Total Parts
To find the share of C, we first need to determine the total parts contributed by A, B, and C. The total parts can be calculated as:
\[ \text{Total parts} = \text{parts of A} + \text{parts of B} + \text{parts of C} \]
Let the parts of C be \( x \). Therefore,
\[ 20 = 5 + 8 + x \]

### Step 3: Solve for the Share of C
Now we can solve for \( x \):
\[ 20 = 13 + x \]
\[ x = 20 - 13 \]
\[ x = 7 \]
So, the share of C is 7 parts.

### Step 4: Calculate the Central Angle for Share of C
The central angle for a sector in a circle can be calculated using the formula:
\[ \text{Central Angle} = \left( \frac{\text{Share of C}}{\text{Total Salary}} \right) \times 360^\circ \]
Substituting the values we have:
\[ \text{Central Angle} = \left( \frac{7}{20} \right) \times 360^\circ \]

### Step 5: Simplify the Calculation
Now we can simplify this:
\[ \text{Central Angle} = \frac{7 \times 360}{20} \]
\[ = \frac{2520}{20} \]
\[ = 126^\circ \]

### Final Answer
The central angle of the sector that represents the share of C is \( 126^\circ \).

---