Question

What is the measure of WX shown in the diagram below

Answer 1

D. The measure of WX is 32 degrees

Explanation:

The correct answer is 32 degrees

Answer 2

D.
`32^(\circ)`

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)=(114^(\circ)-WX)/(2)`

`2*41^(\circ)=(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.