Question

What is the measure of WX shown in the diagram below

Answer 1

Answer:

D. $32^{\circ}$

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:

$m\angle S=\frac{\text{Major Arc-Minor Arc}}{2}$

$41^{\circ}=\frac{114^{\circ}-WX}{2}$

$2*41^{\circ}=\frac{114^{\circ}-WX}{2}*2$

$82^{\circ}=114^{\circ}-WX$

$82^{\circ}-114^{\circ}=114^{\circ}-114^{\circ}-WX$

$-32^{\circ}=-WX$

$WX=32^{\circ}$

Therefore, the measure of arc WX is 32 degrees and option D is the correct choice.