To determine the central angle measure for the Humanities slice in the circle graph, we can follow these steps:
1. Identify the Total Number of Sorority Members: According to the table, the total number of sorority members is 450.
2. Number of Humanities Members: The table shows that there are 126 members majoring in Humanities.
3. Determine the Fraction of Humanities Members: We calculate the fraction of the total members that the Humanities members represent. This is done by dividing the number of Humanities members by the total number of members.
[tex]\[
\text{Fraction of Humanities members} = \frac{126}{450}
\][/tex]
4. Calculate the Central Angle: The total number of degrees in a circle is 360 degrees. To find the central angle measure for the Humanities slice, we multiply the fraction of Humanities members by the total number of degrees.
[tex]\[
x = \left(\frac{126}{450}\right) \times 360
\][/tex]
5. Simplify the Calculation: Evaluating the above expression gives:
[tex]\[
x = \left(\frac{126}{450}\right) \times 360 \approx 100.80000000000001
\][/tex]
Therefore, the central angle measure for the Humanities slice in the circle graph is approximately [tex]\( 100.80000000000001^\circ \)[/tex].
