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what is the best description of angle uvz and angle wvz 

In the given diagram, we are asked to describe angles \( \angle UVZ \) and \( \angle WVZ \).

### Analysis of the Diagram:
- \( \angle UVW \) is a straight line, implying it measures \( 180^\circ \).
- \( \angle UVY \), \( \angle YVZ \), \( \angle ZVS \), and \( \angle SVW \) are angles around point \( V \).
- The right angle (\( 90^\circ \)) is marked at \( \angle UVW \).

### Description of \( \angle UVZ \):
- \( \angle UVZ \) is formed by ray \( VY \) (or \( VZ \)) and ray \( VU \).
- Given \( \angle UVW \) is a straight angle, it is split into smaller angles, including \( \angle UVY \) and \( \angle YVZ \).
- Therefore, \( \angle UVZ \) is the sum of \( \angle UVY \) and \( \angle YVZ \).

### Description of \( \angle WVZ \):
- \( \angle WVZ \) is formed by ray \( VZ \) and ray \( VW \).
- Given \( \angle UVW \) is a straight angle, \( \angle UVY + \angle YVZ + \angle ZVW = 180^\circ \).
- \( \angle WVZ \) is actually \( \angle ZVW \).

### Specific Descriptions:
1. **\( \angle UVZ \)**:
   - This angle is the sum of the angles that make up the right angle and the angle extending from \( V \) through \( Z \).
   - Essentially, it is part of the angles forming the straight line \( UVW \).

2. **\( \angle WVZ \)**:
   - This angle is adjacent to the right angle \( \angle UVW \) and is part of the complementary angles that sum up to the straight angle \( 180^\circ \).
   - Therefore, \( \angle WVZ \) is complementary to the remaining angle not included in \( \angle UVW \).

### Conclusion:
- \( \angle UVZ \) and \( \angle WVZ \) are angles that share common rays with the right angle and together form a straight line with the right angle.

Would you like any further details or have any questions? Here are some additional questions you might find interesting:

1. How would you calculate the measure of \( \angle UVZ \) if \( \angle UVY \) is given as \( 30^\circ \) and \( \angle YVZ \) as \( 60^\circ \)?
2. What is the measure of \( \angle WVZ \) if the measure of \( \angle UVZ \) is \( 90^\circ \)?
3. How do you verify that \( \angle UVW \) is a straight angle?
4. Can you find the measure of \( \angle UVS \)?
5. What are the properties of angles around a point, and how can they be used to solve angle measures?

**Tip:** When dealing with angles on a straight line, always remember that the sum of adjacent angles around a point is \( 180^\circ \).

Explore the properties and measurements of angles UVZ and WVZ in a geometric diagram. Understand how these angles relate to straight lines and angles around a point. Suitable for students in Grades 7-9.

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