The amusement park holds a game of chance in which entrance tickets to the amusement park can be won. At the beginning of the game, one rolls a die whose faces are numbered with the numbers 1 to 6. If one obtains the number 6, one may then spin a wheel of fortune with three sectors once (see schematic diagram). If sector $K$ is obtained, one wins a child ticket worth 28 euros; for sector $E$, an adult ticket worth 36 euros. For sector $N$, one wins nothing. The central angle of sector $N$ is $160 ^ { \circ }$. The sizes of sectors $K$ and $E$ are chosen such that the average winnings per game amount to three euros. Determine the size of the central angles of sectors $K$ and $E$.
The amusement park holds a game of chance in which entrance tickets to the amusement park can be won. At the beginning of the game, one rolls a die whose faces are numbered with the numbers 1 to 6. If one obtains the number 6, one may then spin a wheel of fortune with three sectors once (see schematic diagram). If sector $K$ is obtained, one wins a child ticket worth 28 euros; for sector $E$, an adult ticket worth 36 euros. For sector $N$, one wins nothing. The central angle of sector $N$ is $160 ^ { \circ }$. The sizes of sectors $K$ and $E$ are chosen such that the average winnings per game amount to three euros. Determine the size of the central angles of sectors $K$ and $E$.