Question

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

Answer 1

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

Explanation:

Since, we know that,

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

=
`\frac{\text{major arc - minor arc}}{2}`

Here, Major arc = y°

Minor arc = 116°

And, Angle made by two tangents YX and YZ,

`m\angle XYZ = \frac{\text{y - 116}}{2}`

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

⇒
`\frac{\text{y - 116}}{2} = 64`

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

Thus, Option B is correct.

Answer 2

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

Explanation:

<y = 1/2 (zwyx - zx)

64 = 1/2 (y-116)