Measuring angles using a protractor worksheet.

Problem Analysis:

The task involves measuring the angles formed by rays extending from a common vertex using a protractor. The angles are labeled as \( \angle CAB \), \( \angle DAB \), \( \angle EAB \), \( \angle CAF \), \( \angle DAF \), and \( \angle EAF \). We need to measure each angle in degrees.

Step-by-Step Solution:

#### First Protractor Image:

1. Identify the Vertex and Rays:
- The vertex is point \( A \).
- The rays extend from \( A \) to points \( B, C, D, E, \) and \( F \).

2. Measure Each Angle:
- \( \angle CAB \):
- Place the protractor's center on point \( A \).
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AC \) intersects the protractor.
- From the image, \( \angle CAB = 30^\circ \).

- \( \angle DAB \):
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AD \) intersects the protractor.
- From the image, \( \angle DAB = 60^\circ \).

- \( \angle EAB \):
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AE \) intersects the protractor.
- From the image, \( \angle EAB = 90^\circ \).

- \( \angle CAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AC \) intersects the protractor.
- From the image, \( \angle CAF = 150^\circ \).

- \( \angle DAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AD \) intersects the protractor.
- From the image, \( \angle DAF = 120^\circ \).

- \( \angle EAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AE \) intersects the protractor.
- From the image, \( \angle EAF = 90^\circ \).

3. Record the Measurements:
- \( \angle CAB = 30^\circ \)
- \( \angle DAB = 60^\circ \)
- \( \angle EAB = 90^\circ \)
- \( \angle CAF = 150^\circ \)
- \( \angle DAF = 120^\circ \)
- \( \angle EAF = 90^\circ \)

#### Second Protractor Image:

1. Identify the Vertex and Rays:
- The vertex is point \( A \).
- The rays extend from \( A \) to points \( B, C, D, E, \) and \( F \).

2. Measure Each Angle:
- \( \angle CAB \):
- Place the protractor's center on point \( A \).
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AC \) intersects the protractor.
- From the image, \( \angle CAB = 30^\circ \).

- \( \angle DAB \):
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AD \) intersects the protractor.
- From the image, \( \angle DAB = 60^\circ \).

- \( \angle EAB \):
- Align the 0° mark of the protractor with ray \( AB \).
- Read the angle where ray \( AE \) intersects the protractor.
- From the image, \( \angle EAB = 90^\circ \).

- \( \angle CAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AC \) intersects the protractor.
- From the image, \( \angle CAF = 150^\circ \).

- \( \angle DAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AD \) intersects the protractor.
- From the image, \( \angle DAF = 120^\circ \).

- \( \angle EAF \):
- Align the 0° mark of the protractor with ray \( AF \).
- Read the angle where ray \( AE \) intersects the protractor.
- From the image, \( \angle EAF = 90^\circ \).

3. Record the Measurements:
- \( \angle CAB = 30^\circ \)
- \( \angle DAB = 60^\circ \)
- \( \angle EAB = 90^\circ \)
- \( \angle CAF = 150^\circ \)
- \( \angle DAF = 120^\circ \)
- \( \angle EAF = 90^\circ \)

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{First Image:} & \angle CAB = 30^\circ, \angle DAB = 60^\circ, \angle EAB = 90^\circ, \angle CAF = 150^\circ, \angle DAF = 120^\circ, \angle EAF = 90^\circ \\
\text{Second Image:} & \angle CAB = 30^\circ, \angle DAB = 60^\circ, \angle EAB = 90^\circ, \angle CAF = 150^\circ, \angle DAF = 120^\circ, \angle EAF = 90^\circ
\end{array}
}
\]