If the outer arc is x, the inner arc is 360 - x
[tex]90 = \frac{1}{2}( x - (360 - x) )[/tex]
[tex]90 = \frac{1}{2}( x - 360 + x )[/tex]
[tex]90 = \frac{1}{2}( 2x - 360)[/tex]
[tex]180 = 2x - 360[/tex]
[tex]2x = 360 + 180[/tex]
[tex]2x = 540[/tex]
[tex]x = 270[/tex]
