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In the above diagram, the purple angle at \(Z\) equals \( \color{purple}{ 144}^\circ \) and the blue angle at \(Y\) equals \( \color{blue} {111} ^ \circ \). What is the measure of the green angle at \(X\)?

Note: The diagram is not drawn to scale.

In the above diagram, what is \( \color{green} {\text{green angle}} \) in degrees?

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