To determine the central angle that corresponds to Football, we have to determine what percentage does 416 represent from 1600.
Recall that to determine the percentage that x represents from y, we can use the following expression:
![(x)/(y)*100.](https://img.qammunity.org/2023/formulas/mathematics/college/ytkka7zuzccxasxx6gzbvzxr391vp6pk2h.png)
Therefore, 416 represents
![(416)/(1600)*100=26\%](https://img.qammunity.org/2023/formulas/mathematics/college/mhdb9req2ndwva4kqjmv8cv5snj9zkcbnz.png)
of 1600. Now that same 26% is the percentage of 360° that corresponds to the central angle x, therefore:
![x=360*0.26=93.6.](https://img.qammunity.org/2023/formulas/mathematics/college/brbqniefjxe84hp2qgblbzvhfgnirxggj4.png)
Answer:
![x^(\circ)=93.6^(\circ).](https://img.qammunity.org/2023/formulas/mathematics/college/n8c3oawsmfj8yee2obr6t52roa1yzbq9s4.png)