In an examination of 240 marks, a student scored 52 marks. In pie-chart, the corresponding angle is

Options

A. `63^(@)`
B. `75^(@)`
C. `78^(@)`
D. `(21(2)/(3))`

Answer

To find the corresponding angle in a pie chart for a student's score of 52 marks out of a total of 240 marks, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Marks and the Score**:
- Total marks in the examination = 240
- Marks scored by the student = 52

2. **Formula for Central Angle**:
- The formula to find the central angle corresponding to a particular score in a pie chart is:
\[ \text{Central Angle} = \left( \frac{\text{Score}}{\text{Total Marks}} \right) \times 360 \]

3. **Substituting the Values**:
- Substitute the values into the formula:
\[ \text{Central Angle} = \left( \frac{52}{240} \right) \times 360 \]

4. **Calculating the Fraction**:
- First, simplify the fraction:
\[ \frac{52}{240} = \frac{13}{60} \quad (\text{by dividing both numerator and denominator by 4}) \]

5. **Calculating the Central Angle**:
- Now, substitute the simplified fraction back into the formula:
\[ \text{Central Angle} = \left( \frac{13}{60} \right) \times 360 \]
- Calculate:
\[ \text{Central Angle} = 13 \times 6 = 78 \text{ degrees} \]

6. **Final Answer**:
- The corresponding angle in the pie chart for the student's score is **78 degrees**.