Free Angles worksheets for homeschoolers, students, parents and ... - Free Printable

Problem Overview:

The task involves naming angles based on their vertices and sides, as well as identifying angles in different ways. The worksheet provides diagrams of various angles and asks for specific information about them.

Solution and Explanation:

#### Part 1: Name the vertex and sides of each angle

1. First Diagram (Left Column):
- Vertex: \( C \)
- Sides: \( \overline{CD} \) and \( \overline{CE} \)

2. Second Diagram (Left Column):
- Vertex: \( E \)
- Sides: \( \overline{EA} \) and \( \overline{EN} \)

3. Third Diagram (Right Column):
- Vertex: \( R \)
- Sides: \( \overline{RZ} \) and \( \overline{RM} \)

4. Fourth Diagram (Right Column):
- Vertex: \( S \)
- Sides: \( \overline{SW} \) and \( \overline{SP} \)

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#### Part 2: Name each angle in four ways

1. First Diagram (Left Column):
- Vertex: \( X \)
- Four Names:
- \( \angle X \)
- \( \angle LXC \)
- \( \angle CXO \)
- \( \angle OXF \)

2. Second Diagram (Right Column):
- Vertex: \( K \)
- Four Names:
- \( \angle K \)
- \( \angle JKT \)
- \( \angle TKJ \)
- \( \angle JTK \)

3. Third Diagram (Left Column):
- Vertex: \( Y \)
- Four Names:
- \( \angle Y \)
- \( \angle HYU \)
- \( \angle UYH \)
- \( \angle HUY \)

4. Fourth Diagram (Right Column):
- Vertex: \( I \)
- Four Names:
- \( \angle I \)
- \( \angle BIG \)
- \( \angle GIB \)
- \( \angle BGI \)

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

1. First Diagram (Left Column):
- Vertex: \( V \)
- Angles:
- \( \angle 5 \)
- \( \angle 7 \)
- \( \angle RVX \)

2. Second Diagram (Right Column):
- Vertex: \( V \)
- Angles:
- \( \angle 5 \)
- \( \angle 8 \)
- \( \angle TVN \)

3. Third Diagram (Left Column):
- Vertex: \( V \)
- Angles:
- \( \angle 3 \)
- \( \angle 5 \)
- \( \angle 9 \)
- \( \angle ZVI \)
- \( \angle ZVL \)
- \( \angle RVZ \)

4. Fourth Diagram (Right Column):
- Vertex: \( V \)
- Angles:
- \( \angle 4 \)
- \( \angle 5 \)
- \( \angle 9 \)
- \( \angle KVE \)
- \( \angle KVH \)
- \( \angle WVE \)

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Final Answer:

\[
\boxed{
\text{See detailed explanations above for each part.}
}
\]