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Arc WY - Arc XV = Angle U = 30 degrees.

Arc WY + Arx XV = 360 - 170 - 110 = 80 degrees.

Therefore, arc WY = (30 + 80)/2 = 55 degrees.

Another answer is here

https://web2.0calc.com/questions/help-please_82539

In the diagram, \(\angle U = 30^\circ\), arc XY is \(170^\circ\), and arc VW is \(110^\circ\).

Find arc WY, in degrees.

\(\begin{array}{|rcll|} \hline \mathbf{\text{ In $\triangle $ UWY}} \\ \hline \mathbf{180^\circ} &=& \mathbf{U + \left(90^\circ-\dfrac{170^\circ}{2}+ 90^\circ-\dfrac{WY}{2}\right)} \\ && \quad \mathbf{ +\left(90^\circ-\dfrac{110^\circ}{2}+ 90^\circ-\dfrac{WY}{2} \right)} \\\\ 180^\circ &=& U + \left(180^\circ-85^\circ-\dfrac{WY}{2}\right) \\ && \quad + \left(180^\circ-55^\circ-\dfrac{WY}{2} \right) \\\\ 180^\circ &=& U + 95^\circ-\dfrac{WY}{2} + 125^\circ-\dfrac{WY}{2} \\\\ 180^\circ &=& U + 220^\circ - WY \quad | \quad U=30^\circ \\ 180^\circ &=& 30^\circ + 220^\circ - WY \\ 180^\circ &=& 250^\circ - WY \\ WY &=& 250^\circ - 180^\circ \\ \mathbf{WY} &=& \mathbf{70^\circ} \\ \hline \end{array}\)