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In the figure, four line segments $AB, CD, EF, GH$ intersect at a single point.

Find the value (in degrees) of the angle sum $x + y + w + z.$

$$ Note: $\angle EFH = 55 ^ \circ$, $\angle ACD = 37 ^ \circ$, and $\angle GHF = 85 ^ \circ$.

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