The problem provides a table showing the frequency of meals ordered at a restaurant: Burger (17), Pasta (4), and Soup (9). It asks us to calculate the central angle of the soup section in a pie chart representing this data.

1. Problem Description

The problem provides a table showing the frequency of meals ordered at a restaurant: Burger (17), Pasta (4), and Soup (9). It asks us to calculate the central angle of the soup section in a pie chart representing this data.

2. Solution Steps

First, we need to calculate the total frequency of meals ordered.

$Total Frequency = Burger + Pasta + Soup$

$Total Frequency = 17 + 4 + 9 = 30$

Next, we need to determine the fraction of meals that are soup.

$Soup Fraction = \frac{Frequency of Soup}{Total Frequency} = \frac{9}{30}$

We can simplify this fraction by dividing both numerator and denominator by

3. $Soup Fraction = \frac{9 \div 3}{30 \div 3} = \frac{3}{10}$

Since a full circle (pie chart) has 360 degrees, we can find the central angle for the soup section by multiplying the soup fraction by 360 degrees.

$Soup Angle = Soup Fraction \times 360^{\circ} = \frac{3}{10} \times 360^{\circ}$

$Soup Angle = \frac{3 \times 360}{10}^{\circ} = \frac{1080}{10}^{\circ} = 108^{\circ}$

3. Final Answer

The central angle of the soup section is 108 degrees.