Question

1. look at this angle: name this angle in three different ways: uv+ and tvu and

Explanation:

Step1: Recall angle naming rules

An angle can be named by: 1) Using the vertex letter (if unique), 2) Using three letters with the vertex in the middle, 3) Using a number or symbol (here, the angle at \( V \) with sides \( VU \) and \( VT \)).

Step2: First naming (three - letter, \( V \) in middle)

Using points \( U \), \( V \), \( T \) with \( V \) as vertex: \( \angle UVT \) (or \( \angle TVU \) as the order of the non - vertex points can be reversed).

Step3: Second naming (vertex letter)

Since the angle has vertex \( V \) and no other angle shares this vertex (from the diagram), we can name it \( \angle V \).

Step4: Third naming (three - letter, correct order)

Another three - letter name with \( V \) in the middle: \( \angle UVT \), \( \angle TVU \), and \( \angle V \) (or if we consider the angle symbol with the vertex, but the standard three ways are: using three letters (two rays' points and vertex), using vertex, or using a label. Here, the three valid names are \( \angle UVT \), \( \angle TVU \), and \( \angle V \). But from the diagram, the angle is at \( V \) between \( VU \) and \( VT \), so the three ways are:

1. \( \angle UVT \) (points on the rays and vertex, \( U - V - T \))
2. \( \angle TVU \) (points on the rays and vertex, \( T - V - U \))
3. \( \angle V \) (using the vertex)

Answer:

\( \angle UVT \), \( \angle TVU \), \( \angle V \)