# In the diagram below, xy and yz are tangent to o which expression gives the measure of xyz?

###### Question:

## Answers

The answer is for sure b.

B) 1/2 (154° - 46°)

Step-by-step explanation:

Here ∠XYZ is an angle subtended by two chords from a point outside of the circle.

It is a one of the circle.

If the angle subtended by two chords from the outside point of the circle, the measure of the angle is 1/2 times difference of the major arc and minor arc.

Here Major arc = 154° and minor arc = 46°

Applying the rule, we get

m∠XYZ = [tex]\frac{1}{2} (Major arc - Minor arc)[/tex]

m∠XYZ = 1/2 (154° - 46°)

b

Step-by-step explanation:

You're answer is b. All you have to do is a measurement

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: [tex]\overarc{XWZ}=245^{\circ}[/tex] and[tex]\overarc{XZ}=115^{\circ}[/tex]

Thus, as per the theorem, the measure of the [tex]\angle XYZ[/tex] can be calculated as:

[tex]m\angle XYZ=\frac{1}{2}(\overarc{XWZ}- \overarc{XZ})[/tex]

Therefore, we get:

[tex]m\angle XYZ=\frac{1}{2}(245^{\circ} -115^{\circ})[/tex]

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

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite.

so

[tex]Angle\ XYZ=\frac{1}{2}[arc\ UW+arc\ XZ][/tex]

In this problem we have

[tex]arc\ UW=110\°[/tex]

[tex]arc\ XZ=42\°[/tex]

substitute the values

[tex]Angle\ XYZ=\frac{1}{2}[110\°+42\°][/tex]

therefore

the answer is the option B

[tex]\frac{1}{2}[110\°+42\°][/tex]

The correct answer is B

More information is neede

Not really sure i think its b not sure

Yeah I would say B too.