Question

In the diagram below, XY and YZ are tangent to O which expression gives the measure of XYZ?

Answer 1

the answer is for sure b.

Answer 2

The solution of this question will make use of the Two Tangents from Point Theorem which states that "the measure of an angle formed by two tangents drawn from a point outside the circle is half the the difference of the intercepted arcs".

We can also see that the measure of arcs are:
`\overarc{XWZ}=245^(\circ)` and
`\overarc{XZ}=115^(\circ)`

Thus, as per the theorem, the measure of the
`\angle XYZ` can be calculated as:

`m\angle XYZ=(1)/(2)(\overarc{XWZ}- \overarc{XZ})`

Therefore, we get:

`m\angle XYZ=(1)/(2)(245^(\circ) -115^(\circ))`

Thus, out of the given options, option B is the correct option.