Free printable geometry worksheet for identifying vertices and sides of angles.

To solve the problem, we need to identify the vertex and the sides of each angle in the given diagrams. Let's go through each diagram step by step.

Diagram 1:

- Vertex: The point where the two sides of the angle meet.
- Sides: The two rays that form the angle.

#### Diagram 1:
- Vertex: \( O \)
- Sides: \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \)

Diagram 2:

#### Diagram 2:
- Vertex: \( Q \)
- Sides: \( \overrightarrow{QL} \) and \( \overrightarrow{QM} \)

Diagram 3:

#### Diagram 3:
- Vertex: \( M \)
- Sides: \( \overrightarrow{LM} \) and \( \overrightarrow{MN} \)

Diagram 4:

#### Diagram 4:
- Vertex: \( O \)
- Sides: \( \overrightarrow{OP} \) and \( \overrightarrow{OR} \)

Diagram 5:

#### Diagram 5:
- Vertex: \( X \)
- Sides: \( \overrightarrow{XY} \) and \( \overrightarrow{XZ} \)

Diagram 6:

#### Diagram 6:
- Vertex: \( R \)
- Sides: \( \overrightarrow{RS} \) and \( \overrightarrow{RT} \)

Diagram 7:

#### Diagram 7:
- Vertex: \( V \)
- Sides: \( \overrightarrow{VU} \) and \( \overrightarrow{VW} \)

Diagram 8:

#### Diagram 8:
- Vertex: \( Y \)
- Sides: \( \overrightarrow{YZ} \) and \( \overrightarrow{YX} \)

Final Answers:

1. Vertex: \( O \), Sides: \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \)
2. Vertex: \( Q \), Sides: \( \overrightarrow{QL} \) and \( \overrightarrow{QM} \)
3. Vertex: \( M \), Sides: \( \overrightarrow{LM} \) and \( \overrightarrow{MN} \)
4. Vertex: \( O \), Sides: \( \overrightarrow{OP} \) and \( \overrightarrow{OR} \)
5. Vertex: \( X \), Sides: \( \overrightarrow{XY} \) and \( \overrightarrow{XZ} \)
6. Vertex: \( R \), Sides: \( \overrightarrow{RS} \) and \( \overrightarrow{RT} \)
7. Vertex: \( V \), Sides: \( \overrightarrow{VU} \) and \( \overrightarrow{VW} \)
8. Vertex: \( Y \), Sides: \( \overrightarrow{YZ} \) and \( \overrightarrow{YX} \)

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Diagram 1:} & \text{Vertex: } O, \text{ Sides: } \overrightarrow{OA}, \overrightarrow{OB} \\
\text{Diagram 2:} & \text{Vertex: } Q, \text{ Sides: } \overrightarrow{QL}, \overrightarrow{QM} \\
\text{Diagram 3:} & \text{Vertex: } M, \text{ Sides: } \overrightarrow{LM}, \overrightarrow{MN} \\
\text{Diagram 4:} & \text{Vertex: } O, \text{ Sides: } \overrightarrow{OP}, \overrightarrow{OR} \\
\text{Diagram 5:} & \text{Vertex: } X, \text{ Sides: } \overrightarrow{XY}, \overrightarrow{XZ} \\
\text{Diagram 6:} & \text{Vertex: } R, \text{ Sides: } \overrightarrow{RS}, \overrightarrow{RT} \\
\text{Diagram 7:} & \text{Vertex: } V, \text{ Sides: } \overrightarrow{VU}, \overrightarrow{VW} \\
\text{Diagram 8:} & \text{Vertex: } Y, \text{ Sides: } \overrightarrow{YZ}, \overrightarrow{YX} \\
\end{array}
}
\]