1. Problem: Complete the charts by finding missing percents or angles, ensuring percents total 100% and angles total 360° for each survey. 2. Formula: Use the relationship between percent and angle in a circle graph: $$\text{Angle} = \frac{\text{Percent}}{100} \times 360^\circ$$ or equivalently, $$\text{Percent} = \frac{\text{Angle}}{360^\circ} \times 100$$ 3. Part a) Daily newspaper habit: - Given: Delivered to home = 40%, Never look at = 10%, Buy occasionally angle = 180° - Find percent for buy occasionally: $$\text{Percent} = \frac{180}{360} \times 100 = 50\%$$ - Check percents sum: 40% + 50% + 10% = 100% - Find angle for delivered to home: $$\text{Angle} = \frac{40}{100} \times 360 = 144^\circ$$ - Find angle for never look at: $$\text{Angle} = \frac{10}{100} \times 360 = 36^\circ$$ 4. Part b) How students spend money: - Given: Clothes and personal care = 30%, Savings = 15%, Entertainment angle = 162°, Snacks angle = 36° - Find percent for entertainment: $$\text{Percent} = \frac{162}{360} \times 100 = 45\%$$ - Find percent for snacks: $$\text{Percent} = \frac{36}{360} \times 100 = 10\%$$ - Check percents sum: 45% + 30% + 10% + 15% = 100% - Find angle for clothes and personal care: $$\text{Angle} = \frac{30}{100} \times 360 = 108^\circ$$ - Find angle for savings: $$\text{Angle} = \frac{15}{100} \times 360 = 54^\circ$$ 5. Part c) Favourite kind of pie: - Given: Apple = 20%, Blueberry angle = 54°, Other = 55% - Find percent for blueberry: $$\text{Percent} = \frac{54}{360} \times 100 = 15\%$$ - Sum known percents: 20% + 15% + 55% = 90% - Find percent for cherry: $$100\% - 90\% = 10\%$$ - Find angle for cherry: $$\text{Angle} = \frac{10}{100} \times 360 = 36^\circ$$ Final answers: a) Buy occasionally: 50%, Delivered to home angle: 144°, Never look at angle: 36° b) Entertainment: 45%, Clothes and personal care angle: 108°, Snacks: 10%, Savings angle: 54° c) Blueberry: 15%, Cherry: 10%, Cherry angle: 36° Each circle graph can be drawn by marking these angles as segments of a 360° circle with labels for clarity.