CEMC Gauss (Grade 7), 2020

Solution 1

One complete rotation equals $360\degree$.

Since $90\degree$ is $\frac{90\degree}{360\degree}=\frac14$ of one complete rotation, then $\frac14$ of all students chose juice.

Therefore, the remaining $1-\frac14=\frac34$ of all students chose milk.
Since $\frac34$ is $3\times\frac14$, then $3\times80=240$ students chose milk.

Solution 2

As in Solution 1, $\frac14$ of all students chose juice.

Since the 80 students who chose juice represent $\frac14$ of the total number of students, then the total number of students is $4\times80=320$.
Therefore, $320-80=240$ students chose milk.