Geometry Worksheets | Angles Worksheets - Free Printable

Problem Analysis:

The task involves identifying and naming angles based on their vertices and sides. Let's solve each part step by step.

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Part 1: Name the vertex and sides of each angle

#### 1)
- Vertex: \( O \)
- Sides: \( \overrightarrow{OR} \) and \( \overrightarrow{OM} \)

#### 2)
- Vertex: \( F \)
- Sides: \( \overrightarrow{FE} \) and \( \overrightarrow{FO} \)

#### 3)
- Vertex: \( K \)
- Sides: \( \overrightarrow{KJ} \) and \( \overrightarrow{KL} \)

#### 4)
- Vertex: \( H \)
- Sides: \( \overrightarrow{HO} \) and \( \overrightarrow{HN} \)

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Part 2: Name each angle in four ways

#### 5)
- Vertex: \( O \)
- Sides: \( \overrightarrow{OR} \) and \( \overrightarrow{OS} \)
- Four ways to name the angle:
1. \( \angle ROS \)
2. \( \angle SOR \)
3. \( \angle R \)
4. \( \angle O \)

#### 6)
- Vertex: \( M \)
- Sides: \( \overrightarrow{ML} \) and \( \overrightarrow{MN} \)
- Four ways to name the angle:
1. \( \angle LMN \)
2. \( \angle NML \)
3. \( \angle M \)
4. \( \angle LNM \)

#### 7)
- Vertex: \( N \)
- Sides: \( \overrightarrow{NO} \) and \( \overrightarrow{NP} \)
- Four ways to name the angle:
1. \( \angle ONP \)
2. \( \angle PNO \)
3. \( \angle N \)
4. \( \angle NOP \)

#### 8)
- Vertex: \( K \)
- Sides: \( \overrightarrow{KL} \) and \( \overrightarrow{KM} \)
- Four ways to name the angle:
1. \( \angle LKM \)
2. \( \angle MKL \)
3. \( \angle K \)
4. \( \angle LMK \)

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Part 3: Name all the angles that have \( V \) as a vertex

#### 9)
- Vertex: \( V \)
- Angles with vertex \( V \):
- \( \angle DVE \)
- \( \angle EVF \)
- \( \angle FVD \)

#### 10)
- Vertex: \( V \)
- Angles with vertex \( V \):
- \( \angle QVR \)
- \( \angle RVS \)
- \( \angle SVQ \)

#### 11)
- Vertex: \( V \)
- Angles with vertex \( V \):
- \( \angle XVZ \)
- \( \angle ZVY \)
- \( \angle YVX \)

#### 12)
- Vertex: \( V \)
- Angles with vertex \( V \):
- \( \angle KVJ \)
- \( \angle JVZ \)
- \( \angle ZVK \)

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Final Answers:

1. Vertex: \( O \), Sides: \( \overrightarrow{OR}, \overrightarrow{OM} \)
2. Vertex: \( F \), Sides: \( \overrightarrow{FE}, \overrightarrow{FO} \)
3. Vertex: \( K \), Sides: \( \overrightarrow{KJ}, \overrightarrow{KL} \)
4. Vertex: \( H \), Sides: \( \overrightarrow{HO}, \overrightarrow{HN} \)

5. \( \angle ROS, \angle SOR, \angle R, \angle O \)
6. \( \angle LMN, \angle NML, \angle M, \angle LNM \)
7. \( \angle ONP, \angle PNO, \angle N, \angle NOP \)
8. \( \angle LKM, \angle MKL, \angle K, \angle LMK \)

9. \( \angle DVE, \angle EVF, \angle FVD \)
10. \( \angle QVR, \angle RVS, \angle SVQ \)
11. \( \angle XVZ, \angle ZVY, \angle YVX \)
12. \( \angle KVJ, \angle JVZ, \angle ZVK \)

\boxed{
\begin{array}{l}
\text{1) Vertex: } O, \text{ Sides: } \overrightarrow{OR}, \overrightarrow{OM} \\
\text{2) Vertex: } F, \text{ Sides: } \overrightarrow{FE}, \overrightarrow{FO} \\
\text{3) Vertex: } K, \text{ Sides: } \overrightarrow{KJ}, \overrightarrow{KL} \\
\text{4) Vertex: } H, \text{ Sides: } \overrightarrow{HO}, \overrightarrow{HN} \\
\text{5) } \angle ROS, \angle SOR, \angle R, \angle O \\
\text{6) } \angle LMN, \angle NML, \angle M, \angle LNM \\
\text{7) } \angle ONP, \angle PNO, \angle N, \angle NOP \\
\text{8) } \angle LKM, \angle MKL, \angle K, \angle LMK \\
\text{9) } \angle DVE, \angle EVF, \angle FVD \\
\text{10) } \angle QVR, \angle RVS, \angle SVQ \\
\text{11) } \angle XVZ, \angle ZVY, \angle YVX \\
\text{12) } \angle KVJ, \angle JVZ, \angle ZVK \\
\end{array}
}