Answer:
[tex]\overset{\frown}{WX}= 66^{\circ}[/tex]
Step-by-step explanation:
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of the intercepted arc.
First, use the Inscribed Angle Theorem to calculate the measure of arc WY.
[tex]\displaystyle \angle WXY=\dfrac{1}{2} \overset{\frown}{WY}[/tex]
[tex]\implies 57^{\circ}=\dfrac{1}{2} \overset{\frown}{WY}[/tex]
[tex]\implies \overset{\frown}{WY}= 2 \cdot 57^{\circ}[/tex]
[tex]\implies \overset{\frown}{WY}= 114^{\circ}[/tex]
Assuming XY is the diameter of the circle:
[tex]\implies \overset{\frown}{WY}+ \overset{\frown}{WX}= 180^{\circ}[/tex]
[tex]\implies 114^{\circ} + \overset{\frown}{WX}= 180^{\circ}[/tex]
[tex]\implies \overset{\frown}{WX}= 180^{\circ} - 114^{\circ}[/tex]
[tex]\implies \overset{\frown}{WX}= 66^{\circ}[/tex]
