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Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees. In the diagram of circle A, what is the measure of ∠XYZ? 35° 70° 75° 140°

Circle A is shown Secant W Y intersects tangent Z Y at point Y outside of the circle Secant W Y intersects circle A at point X Arc X Z is 105 degrees and arc W class=

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simrahali15

Answer:

35

Step-by-step explanation:

Here, we can use use the formula for an angle formed by secants or tangents theorem. The formula is

m∠1= [tex]\frac{1}{2} (x-y)[/tex]

In circle A,

m∠1 = ∠XYZ

x = arc WZ

y = arc XZ

m∠1= 1/2 (175-105) degrees

= 35 degrees

The measure of ∠XYZ is 35°.

What is secants theorem?

Secants theorem states that, the angle formed by the two secants which intersect inside the circle is half the sum of the intercepted arcs.

According to Secants theorem,

∠XYZ = ½(arc WZ - arc XZ)

Given, arc WZ = 175° and arc XZ = 105°

Thus;

∠XYZ = ½(175 - 105)

∠XYZ = ½(70)

∠XYZ = 35°

Learn more about Secants theorem here:

https://brainly.com/question/12453038

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