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:
[tex]\frac{x}{y}*100.[/tex]
Therefore, 416 represents
[tex]\frac{416}{1600}*100=26\%[/tex]
of 1600. Now that same 26% is the percentage of 360° that corresponds to the central angle x, therefore:
[tex]x=360*0.26=93.6.[/tex]
Answer:
[tex]x^{\circ}=93.6^{\circ}.[/tex]
