An Angle Discovery!

Geometry Level 4

Given that XYXY is the diameter of the circle, where WXY\triangle WXY is enclosed in the circle and that the ratio AreaofcircleAreaofWXY=2π\frac { Area\quad of\quad circle }{ Area\quad of\quad \triangle WXY } =2\pi.

Find the acute angle WXYWXY. Giving your answer in degrees.

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