Question

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 Z is 175 degrees.

In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°

Answer 1

By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.

How to determine angle <XYZ?

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.

What is the theorem of intersecting secants?

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle XYZ will be given by this formula:

<XYZ = ½ × (m<WZ - m<XZ)

Substituting the given parameters into the formula, we have;

<XYZ = ½ × (175 - 105)

<XYZ = ½ × 70

<XYZ = 35°.

By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.

Read more on intersecting secants here: https://brainly.com/question/1626547

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