The measure of the central angle of the sector representing number of students whose favorite subject is Math is

Options

A. `62^@`
B. `52^@`
C. `42^@`
D. `72^@`

Answer

To find the measure of the central angle of the sector representing the number of students whose favorite subject is Math, we can follow these steps:

### Step 1: Identify the number of students who like Math.
From the information provided, the number of students whose favorite subject is Math is given as 800.

### Step 2: Calculate the total number of respondents.
We need to sum up the number of students who like each subject:
- Math: 800
- Reasoning: 1200
- English: 650
- GS: 750
- Computer: 700
- Hindi: 1400

Calculating the total:
\[ 800 + 1200 + 650 + 750 + 700 + 1400 = 5500 \]
So, the total number of respondents is 5500.

### Step 3: Calculate the central angle for the Math sector.
The formula to find the central angle (in degrees) for a sector in a pie chart is:
\[ \text{Central Angle} = \left( \frac{\text{Number of students for the subject}}{\text{Total number of respondents}} \right) \times 360 \]

Substituting the values:
\[ \text{Central Angle} = \left( \frac{800}{5500} \right) \times 360 \]

### Step 4: Perform the calculation.
First, calculate the fraction:
\[ \frac{800}{5500} = 0.14545454545454545 \]

Now multiply by 360:
\[ 0.14545454545454545 \times 360 = 52.36363636363636 \]

### Step 5: Round the result.
The central angle is approximately 52.36 degrees. Rounding this gives us:
\[ \text{Central Angle} \approx 52 \text{ degrees} \]

### Final Answer:
The measure of the central angle of the sector representing the number of students whose favorite subject is Math is approximately **52 degrees**.

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