1. **State the problem:** We have shoe size frequencies for sizes 4, 5, and 6 from a total of 40 people. The frequencies for sizes 4 and 6 are 20 and 7 respectively, but the frequency for size 5 is missing. We need to find the central angle of the pie chart section representing shoe size 5. 2. **Find the missing frequency:** The total frequency is 40. Given frequencies are: - Size 4: 20 - Size 6: 7 - Size 5: unknown, call it $x$ The sum of frequencies must be 40: $$20 + x + 7 = 40$$ 3. **Solve for $x$:** $$x = 40 - 20 - 7 = 13$$ 4. **Calculate the central angle for size 5:** The central angle in a pie chart is proportional to the frequency: $$\text{Central angle} = \frac{\text{Frequency}}{\text{Total frequency}} \times 360^\circ$$ For size 5: $$\frac{13}{40} \times 360^\circ = 117^\circ$$ **Final answer:** The central angle for shoe size 5 is $117^\circ$.