To determine the angle for the wedge representing the students who prefer honey mustard in a circle graph, follow these steps:
1. Determine the total number of students. In this case, the total number of students is 70.
2. Determine the number of students who prefer honey mustard. According to the data, 10 students prefer honey mustard.
3. Calculate the percentage of students who prefer honey mustard.
[tex]\[
\text{Percentage} = \frac{\text{Number of students who prefer honey mustard}}{\text{Total number of students}} \times 100
\][/tex]
[tex]\[
\text{Percentage} = \frac{10}{70} \times 100 \approx 14.29\%
\][/tex]
4. Calculate the angle for the wedge. Since a circle represents 360 degrees, we use the percentage to find the proportional angle.
[tex]\[
\text{Angle} = \text{Percentage} \times \frac{360}{100}
\][/tex]
[tex]\[
\text{Angle} = 14.29 \times 3.6 \approx 51.4^\circ
\][/tex]
Therefore, the angle for the wedge that represents the students who prefer honey mustard is [tex]\( 51.4^\circ \)[/tex].
The answer is [tex]\( B. \)[/tex] [tex]\( 51.4^\circ \)[/tex].
