1. **State the problem:** We need to find the central angle measure $x^\circ$ for the Bowerman slice in a circle graph representing votes. 2. **Formula:** The central angle for a slice in a circle graph is given by: $$x = \frac{\text{Number of votes for candidate}}{\text{Total votes}} \times 360^\circ$$ 3. **Given data:** - Bowerman votes = 510 - Total votes = 5100 4. **Calculate the fraction of votes for Bowerman:** $$\frac{510}{5100} = \frac{\cancel{510} \times 1}{\cancel{510} \times 10} = \frac{1}{10}$$ 5. **Calculate the central angle:** $$x = \frac{1}{10} \times 360^\circ = 36^\circ$$ 6. **Answer:** The central angle measure for Bowerman's slice is $36^\circ$.