Identify the measure of arc XY◠. PLEASE HELP!!

Use the intersecting chords theorem: the labeled angle (WVZ) between the given chords has measure that is the average of the two arcs the chords intercept (WZ and XY):
[tex]81^\circ=\dfrac{m\widehat{XY}+52^\circ}2\implies m\widehat{XY}=110^\circ[/tex]