Answer key for measuring angles using a protractor, featuring two sets of angle measurements with solutions provided.

The task involves measuring angles using a protractor. The worksheet provides diagrams with labeled points and asks for the measure of each angle in degrees. Below is a detailed explanation of how to solve such problems, along with the solution for the given worksheet.

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General Steps to Measure Angles Using a Protractor:

1. Identify the Vertex: Locate the vertex of the angle (the point where the two rays meet).
2. Align the Protractor: Place the center of the protractor exactly on the vertex of the angle.
3. Align One Ray: Align one ray of the angle with the zero line of the protractor. Ensure that the zero line is along one of the rays.
4. Read the Angle: Look at the scale on the protractor that starts from zero (where the ray is aligned). Follow the second ray to read the angle measurement where it intersects the protractor's scale.
- Use the inner scale if the angle opens to the right.
- Use the outer scale if the angle opens to the left.
5. Record the Measurement: Write down the angle measurement in degrees.

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Solution for the Worksheet:

#### First Diagram:
The first diagram shows a protractor with several rays extending from a common vertex. Each angle is labeled with three letters, where the middle letter represents the vertex.

1. ∠BAF:
- Vertex: A
- Ray BA aligns with the 0° mark on the protractor.
- Ray AF extends to the 141° mark on the outer scale.
- Answer: ∠BAF = 141°

2. ∠CAG:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AG extends to the 159° mark on the outer scale.
- Answer: ∠CAG = 159°

3. ∠BAD:
- Vertex: A
- Ray BA aligns with the 0° mark on the protractor.
- Ray AD extends to the 44° mark on the outer scale.
- Answer: ∠BAD = 44°

4. ∠FAG:
- Vertex: A
- Ray FA aligns with the 0° mark on the protractor.
- Ray AG extends to the 39° mark on the outer scale.
- Answer: ∠FAG = 39°

5. ∠CAD:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AD extends to the 23° mark on the outer scale.
- Answer: ∠CAD = 23°

6. ∠EAF:
- Vertex: A
- Ray EA aligns with the 0° mark on the protractor.
- Ray AF extends to the 35° mark on the outer scale.
- Answer: ∠EAF = 35°

7. ∠DAG:
- Vertex: A
- Ray DA aligns with the 0° mark on the protractor.
- Ray AG extends to the 136° mark on the outer scale.
- Answer: ∠DAG = 136°

8. ∠CAE:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AE extends to the 85° mark on the outer scale.
- Answer: ∠CAE = 85°

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#### Second Diagram:
The second diagram follows the same process as the first one.

1. ∠DAH:
- Vertex: A
- Ray DA aligns with the 0° mark on the protractor.
- Ray AH extends to the 111° mark on the outer scale.
- Answer: ∠DAH = 111°

2. ∠BAG:
- Vertex: A
- Ray BA aligns with the 0° mark on the protractor.
- Ray AG extends to the 171° mark on the outer scale.
- Answer: ∠BAG = 171°

3. ∠FAH:
- Vertex: A
- Ray FA aligns with the 0° mark on the protractor.
- Ray AH extends to the 31° mark on the outer scale.
- Answer: ∠FAH = 31°

4. ∠DAF:
- Vertex: A
- Ray DA aligns with the 0° mark on the protractor.
- Ray AF extends to the 80° mark on the outer scale.
- Answer: ∠DAF = 80°

5. ∠CAF:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AF extends to the 98° mark on the outer scale.
- Answer: ∠CAF = 98°

6. ∠EAF:
- Vertex: A
- Ray EA aligns with the 0° mark on the protractor.
- Ray AF extends to the 65° mark on the outer scale.
- Answer: ∠EAF = 65°

7. ∠CAG:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AG extends to the 120° mark on the outer scale.
- Answer: ∠CAG = 120°

8. ∠CAH:
- Vertex: A
- Ray CA aligns with the 0° mark on the protractor.
- Ray AH extends to the 129° mark on the outer scale.
- Answer: ∠CAH = 129°

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Final Answer:

The answers are already filled in the worksheet, but here they are summarized:

#### First Diagram:
- ∠BAF = 141°
- ∠CAG = 159°
- ∠BAD = 44°
- ∠FAG = 39°
- ∠CAD = 23°
- ∠EAF = 35°
- ∠DAG = 136°
- ∠CAE = 85°

#### Second Diagram:
- ∠DAH = 111°
- ∠BAG = 171°
- ∠FAH = 31°
- ∠DAF = 80°
- ∠CAF = 98°
- ∠EAF = 65°
- ∠CAG = 120°
- ∠CAH = 129°

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{First Diagram:} & \text{Second Diagram:} \\
\hline
\angle BAF = 141^\circ & \angle DAH = 111^\circ \\
\angle CAG = 159^\circ & \angle BAG = 171^\circ \\
\angle BAD = 44^\circ & \angle FAH = 31^\circ \\
\angle FAG = 39^\circ & \angle DAF = 80^\circ \\
\angle CAD = 23^\circ & \angle CAF = 98^\circ \\
\angle EAF = 35^\circ & \angle EAF = 65^\circ \\
\angle DAG = 136^\circ & \angle CAG = 120^\circ \\
\angle CAE = 85^\circ & \angle CAH = 129^\circ \\
\end{array}
}
\]