1. **Stating the problem:** We have a group of 150 referees choosing different sports. The pie chart sectors are given as follows: - Volleyball: 22% of the group - Softball: 59° sector angle - Tennis: 64.8° sector angle - Basketball: 97.2° sector angle - Sater: 11° sector angle - Cricket: sector angle unknown We need to find: (a) Number of persons choosing volleyball (b) Percentage choosing softball (c) Percentage choosing basketball (d) Sector angle size for cricket 2. **Important formulas and rules:** - Total degrees in a circle: $$360^\circ$$ - Percentage to number: $$\text{number} = \text{percentage} \times \text{total}$$ - Sector angle to percentage: $$\text{percentage} = \frac{\text{sector angle}}{360^\circ} \times 100$$ - Sum of all sector angles must be $$360^\circ$$ 3. **Calculations:** (a) Volleyball number: $$\text{Volleyball} = 22\% \times 150 = \frac{22}{100} \times 150 = 33$$ (b) Softball percentage: Given sector angle $$59^\circ$$, so $$\text{Softball percentage} = \frac{59}{360} \times 100 = 16.39\%$$ (c) Basketball percentage: Given sector angle $$97.2^\circ$$, so $$\text{Basketball percentage} = \frac{97.2}{360} \times 100 = 27\%$$ (d) Cricket sector angle: Sum of known sector angles: $$22\% \text{ volleyball} = 22\% \times 360^\circ = 79.2^\circ$$ But volleyball is given as percentage, so convert to degrees: $$22\% \times 360^\circ = 79.2^\circ$$ Sum of known angles: $$59 + 64.8 + 97.2 + 11 + 79.2 = 311.2^\circ$$ Remaining angle for cricket: $$360 - 311.2 = 48.8^\circ$$ **Final answers:** - (a) 33 persons choose volleyball - (b) 16.39% choose softball - (c) 27% choose basketball - (d) Cricket sector angle is 48.8°