To determine the angle for the barbecue wedge in the circle graph, we need to follow a series of steps. Here's the detailed solution:
1. Total Number of People in the Class:
The total number of people surveyed is 70.
2. Number of People Who Prefer Barbecue Sauce:
Out of these, 20 people prefer barbecue sauce.
3. Finding the Fraction:
To find the fraction of the total that prefers barbecue sauce, we divide the number of barbecue sauce fans by the total number of people:
[tex]\[
\text{Fraction of people who prefer barbecue sauce} = \frac{20}{70}
\][/tex]
4. Simplifying the Fraction:
[tex]\[
\frac{20}{70} = \frac{20 \div 10}{70 \div 10} = \frac{2}{7} \approx 0.2857
\][/tex]
5. Determining the Angle:
Since a circle graph (or pie chart) has a total angle of 360 degrees, we multiply the fraction we just found by 360 to determine the size of the angle for barbecue sauce:
[tex]\[
\text{Angle for barbecue wedge} = 0.2857 \times 360 \approx 102.857 \text{ degrees}
\][/tex]
6. Rounding to the Nearest Whole Number:
[tex]\[
102.857 \approx 103 \text{ degrees}
\][/tex]
Therefore, the angle that the wedge for barbecue sauce should have is [tex]\(103^{\circ}\)[/tex].
Hence, the correct answer is:
[tex]\[ \boxed{103^{\circ}} \][/tex]
