Question

warm - up 1 - 4
use the figure at the right.

1. name the vertex of \\( \angle 4 \\).
2. name the sides of \\( \angle 3 \\).
3. what is another name for \\( \angle 2 \\)?
4. what is another name for \\( \angle uxy \\)?

Explanation:

1. The vertex of an angle is the common endpoint of its sides. For \(\angle4\), the vertex is \(U\).
2. The sides of an angle are the two rays that form the angle. For \(\angle3\), the sides are \(\overrightarrow{XW}\) and \(\overrightarrow{XU}\).
3. An angle can be named by its vertex (if there is only one angle at that vertex) or by three points (with the vertex in the middle). For \(\angle2\), another name is \(\angle ZYU\) (since \(Y\) is the vertex and \(Z\) and \(U\) are points on the sides).
4. For \(\angle UXY\), another name is \(\angle1\) (as it is the angle marked as \(1\) in the figure).

Answer:

1. \(U\)
2. \(\overrightarrow{XW}\) and \(\overrightarrow{XU}\)
3. \(\angle ZYU\)
4. \(\angle1\)