Circle graph

Erica surveyed students at her school about their favorite type of music. She made a circle graph to show the results. The central angle for the section of the graph that represents country music measures 72°. If 45 classmates chose the country as their favorite type of music, how many students did Erica survey?

Correct answer:

n =  225

Step-by-step explanation:

$$\begin{gathered} \alpha =72{}^{\circ } \\ {n}_1=45 \\ \Phi =360{}^{\circ } \\ \alpha \dots .n_1 \\ \Phi \dots ..n \\ n:n_1=\Phi :\alpha \\ n=n_1\cdot \frac{\Phi }{\alpha }=45\cdot \frac{360}{72}=\frac{45\cdot 360}{72}=\frac{16200}{72}=225 \end{gathered}$$

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