In a pie graph, a component is represented as a sector with sector angle `96^(@),` then find the percentage of the component value in total.

Options

A. `23 (1)/(3) %`
B. `28 (1)/(3)%`
C. `25 (1)/(3)%`
D. `26 ^(2)/(3)%`

Answer

To find the percentage of the component value represented by a sector with a sector angle of 96 degrees in a pie graph, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Angle of the Pie Chart:**
The total angle in a pie chart is always 360 degrees.

2. **Set Up the Formula for Percentage:**
The percentage of the component value can be calculated using the formula:
\[ \text{Percentage} = \left( \frac{\text{Sector Angle}}{\text{Total Angle}} \right) \times 100 \]

3. **Substitute the Values:**
Here, the sector angle is 96 degrees and the total angle is 360 degrees. Substitute these values into the formula:
\[ \text{Percentage} = \left( \frac{96}{360} \right) \times 100 \]

4. **Simplify the Fraction:**
To simplify \(\frac{96}{360}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 36:
\[ \frac{96 \div 36}{360 \div 36} = \frac{8}{30} \]

5. **Convert to Percentage:**
Now, substitute back into the percentage formula:
\[ \text{Percentage} = \left( \frac{8}{30} \right) \times 100 \]

6. **Calculate the Result:**
To calculate \(\frac{8 \times 100}{30}\):
\[ \text{Percentage} = \frac{800}{30} = 26.6667 \]

7. **Convert to Fraction:**
This can also be expressed as:
\[ 26 \frac{2}{3} \text{ percent} \]

### Final Answer:
The percentage of the component value in total is \(26 \frac{2}{3}\%\).