1. **State the problem:** We have a survey of 90 cars with frequencies for Black, White, and Other colors. We need to complete the table by finding the pie chart sector angles for each color and then complete the pie chart. 2. **Formula for pie chart sector angle:** The angle for each sector is proportional to the frequency. The formula is: $$\text{Sector angle} = \frac{\text{Frequency}}{\text{Total frequency}} \times 360^\circ$$ 3. **Calculate sector angles:** - For Black cars: $$\frac{16}{90} \times 360^\circ = \frac{16 \times 360}{90} = \frac{5760}{90} = 64^\circ$$ - For White cars: $$\frac{34}{90} \times 360^\circ = \frac{34 \times 360}{90} = \frac{12240}{90} = 136^\circ$$ - For Other cars: $$\frac{40}{90} \times 360^\circ = \frac{40 \times 360}{90} = \frac{14400}{90} = 160^\circ$$ 4. **Check sum of angles:** $$64^\circ + 136^\circ + 160^\circ = 360^\circ$$ which confirms the calculations are correct. 5. **Complete the table:** | Colour | Frequency | Pie chart sector angle | |--------|-----------|-----------------------| | Black | 16 | 64° | | White | 34 | 136° | | Other | 40 | 160° | 6. **Complete the pie chart:** - Start from the vertical radius line pointing up (0°). - Draw the Black sector of 64° clockwise from 0° to 64°. - Then draw the White sector of 136° from 64° to 200°. - Finally, draw the Other sector of 160° from 200° to 360° (back to the start). This completes the pie chart accurately representing the survey data.