WAEC Mathematics 2015 Paper

Concept:A pie chart represents the whole population as a full circle of $360^\circ$.A part of the population is represented by a proportional sectoral angle.Explanation:Total population of the school is $810$.The class has $72$ students.The fraction of the total population for this class is $\frac{72}{810}$.Multiply this fraction by the total angle of a circle, $360^\circ$.The sectoral angle is:$$\frac{72}{810} \times 360^\circ$$Simplify the fraction:$$\frac{72}{810} = \frac{4}{45}$$Now multiply:$$\frac{4}{45} \times 360^\circ = \frac{4 \times 360}{45}$$$$\frac{1440}{45} = 32^\circ$$Answer:The sectoral angle for the class is $32^\circ$, which matches option A.