Answer:
D. [tex]32^{\circ}[/tex]
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the measure of arc WX.
Upon looking at our given diagram, we can see that angle S is formed by intersecting secants outside the circle.
We will use intersecting secants theorem, which states that measure of an angle formed by two intersecting secants outside a circle is half the difference of intercepted arcs.
Using above theorem, we can set an equation to find the measure of arc WX as:
[tex]m\angle S=\frac{\text{Major Arc-Minor Arc}}{2}[/tex]
[tex]41^{\circ}=\frac{114^{\circ}-WX}{2}[/tex]
[tex]2*41^{\circ}=\frac{114^{\circ}-WX}{2}*2[/tex]
[tex]82^{\circ}=114^{\circ}-WX[/tex]
[tex]82^{\circ}-114^{\circ}=114^{\circ}-114^{\circ}-WX[/tex]
[tex]-32^{\circ}=-WX[/tex]
[tex]WX=32^{\circ}[/tex]
Therefore, the measure of arc WX is 32 degrees and option D is the correct choice.
