https://file.aiquickdraw.com/mathbot/file/1726260851441xdqo4bi6.jpg

The problem involves identifying the true relationship between the angles in the diagram, specifically angles \( \angle WXY \), \( \angle WXZ \), and \( \angle YXZ \). Based on the image:

- \( X \) is a common vertex for all the angles.
- \( \overrightarrow{WX} \) and \( \overrightarrow{XY} \) form \( \angle WXY \).
- \( \overrightarrow{WX} \) and \( \overrightarrow{XZ} \) form \( \angle WXZ \).
- \( \overrightarrow{XY} \) and \( \overrightarrow{XZ} \) form \( \angle YXZ \).

From the geometry, it seems that \( Z \) lies on the interior of \( \angle WXY \), which suggests that:
- \( \angle WXY \) is the larger angle, and the sum of \( \angle WXZ + \angle YXZ = \angle WXY \).
- The measure of \( \angle WXZ \) is twice that of \( \angle YXZ \), as the point \( Z \) seems to divide the angle into two proportional parts.

Let's evaluate the statements:

1. \( m \angle WXZ = 2(m \angle YXZ) \): This looks like the correct relationship based on the diagram, as \( \angle WXZ \) appears to be double \( \angle YXZ \).
2. \( m \angle WXY = m \angle WXZ \): This would mean that the two angles are equal, which is not likely true because \( \angle WXY \) is larger.
3. \( \frac{1}{2}(m \angle WXY) = m \angle WXZ \): This is incorrect because \( \angle WXZ \) isn't half of \( \angle WXY \).
4. \( 2(m \angle WXZ) = m \angle YXZ \): This is false, as it implies that \( \angle WXZ \) is smaller than \( \angle YXZ \).

The correct answer is:

- **\( m \angle WXZ = 2(m \angle YXZ) \)**.

Would you like further clarification or have any other questions? Here are 5 related questions for practice:

1. What is the sum of the angles \( \angle WXZ + \angle YXZ \)?
2. How can you determine the exact measure of each angle using a protractor?
3. If \( m \angle WXY = 90^\circ \), what are the measures of \( \angle WXZ \) and \( \angle YXZ \)?
4. How would you calculate the measure of \( \angle WXZ \) if you know \( \angle YXZ \)?
5. What is the geometric property that relates the three angles in this diagram?

**Tip:** Always check if angles are being divided proportionally when a point lies on the interior of another angle.

Which of the following statements is true about the relationship between angles \( \angle WXY \), \( \angle WXZ \), and \( \angle YXZ \)?

This geometry problem involves determining the correct relationship between three angles formed by vectors W, X, Y, and Z. Using the Angle Addition Postulate, we deduce that the angle \( m \angle WXZ \) is twice \( m \angle YXZ \). Suitable for high school students studying geometry.

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