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:

$m\angle XYZ=\frac{1}{2}(\overarc{XWZ}- \overarc{XZ})$

Therefore, we get:

$m\angle XYZ=\frac{1}{2}(245^{\circ} -115^{\circ})$

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