Naming Angles Worksheets - Free Printable

To solve the problem of naming angles using three points, we need to follow these steps:

Steps to Name Angles Using Three Points:

1. Identify the Vertex: The vertex is the point where the two rays (or sides) of the angle meet. This is the central point in the name of the angle.
2. Choose the Other Two Points: Select one point from each ray extending from the vertex. These points should be on either side of the vertex.
3. Order the Points: Write the name of the angle by listing the three points in order:
- Start with a point on one ray.
- Follow with the vertex (the middle point).
- End with a point on the other ray.

The general format for naming an angle using three points is: ∠XYZ, where:
- X and Z are points on the rays.
- Y is the vertex.

Solution for Each Angle:

#### Problem 1:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( A \), \( B \), and \( C \).
- Angle Name: \( \angle ABC \)

#### Problem 2:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( D \), \( E \), and \( F \).
- Angle Name: \( \angle DEF \)

#### Problem 3:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( G \), \( H \), and \( I \).
- Angle Name: \( \angle GHI \)

#### Problem 4:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( J \), \( K \), and \( L \).
- Angle Name: \( \angle JKL \)

#### Problem 5:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( M \), \( N \), and \( O \).
- Angle Name: \( \angle MNO \)

#### Problem 6:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( P \), \( Q \), and \( R \).
- Angle Name: \( \angle PQR \)

#### Problem 7:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( S \), \( T \), and \( U \).
- Angle Name: \( \angle STU \)

#### Problem 8:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( V \), \( W \), and \( X \).
- Angle Name: \( \angle VWX \)

#### Problem 9:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( Y \), \( Z \), and \( A' \).
- Angle Name: \( \angle YZA' \)

#### Problem 10:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( B' \), \( C' \), and \( D' \).
- Angle Name: \( \angle B'C'D' \)

#### Problem 11:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( E' \), \( F' \), and \( G' \).
- Angle Name: \( \angle E'F'G' \)

#### Problem 12:
- Vertices and Points: The vertex is at the center, and there are points labeled as \( H' \), \( I' \), and \( J' \).
- Angle Name: \( \angle H'I'J' \)

Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad \angle ABC \\
2. & \quad \angle DEF \\
3. & \quad \angle GHI \\
4. & \quad \angle JKL \\
5. & \quad \angle MNO \\
6. & \quad \angle PQR \\
7. & \quad \angle STU \\
8. & \quad \angle VWX \\
9. & \quad \angle YZA' \\
10. & \quad \angle B'C'D' \\
11. & \quad \angle E'F'G' \\
12. & \quad \angle H'I'J'
\end{aligned}
}
\]