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PLEASE HELP

In the diagram below, XY and YZ are tangent to O. Which equation could be solved to find y, the measure of XWZ?

A. 1/2(y - 64) = 116
B. 1/2(y - 116) = 64
C. 1/2(y + 116) = 64
D. 1/2(y + 64) = 116

PLEASE HELP In the diagram below XY and YZ are tangent to O Which equation could be solved to find y the measure of XWZA 12y 64 116B 12y 116 64C 12y 116 64D 12y class=

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Answer:

B. 1/2(y - 116) = 64

Step-by-step explanation:

<y = 1/2 (zwyx - zx)

64 = 1/2 (y-116)

Answer:  B. 1/2(y - 116) = 64    

Step-by-step explanation:

Since, we know that,

The angle formed by two tangent = [tex]\frac{1}{2}(\text{Difference of intercepted Arcs} )[/tex]  

= [tex]\frac{\text{major arc - minor arc}}{2}[/tex]

Here, Major arc = y°

Minor arc = 116°

And, Angle made by two tangents YX and YZ,

[tex]m\angle XYZ = \frac{\text{y - 116}}{2}[/tex]

[tex]64 = \frac{\text{y - 116}}{2}[/tex]  ( because,  [tex]m\angle XYZ = 64^{\circ}[/tex] )

⇒ [tex]\frac{\text{y - 116}}{2} = 64[/tex]

Which is the required equation to find y,  the measure of XWZ.

Thus, Option B is correct.

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