https://file.aiquickdraw.com/mathbot/file/1726015298980fhjo9j2a.jpg

To solve the given problem, we will need to use the protractor to measure two angles:

1. \(\angle PQS\)
2. \(\angle RQS\)

### Step-by-Step Process:
1. Align the protractor so that the vertex \( Q \) is at the center of the protractor.
2. Ensure that the line \( \overrightarrow{QR} \) aligns with the 0-degree mark on the protractor for accurate measurements.
3. Measure \(\angle PQS\): Locate point \( P \) on the protractor and read the corresponding degree.
4. Measure \(\angle RQS\): Similarly, locate point \( R \) on the protractor and note down the angle formed between \( R \), \( Q \), and \( S \).
5. Add the two angles together to find their sum.

Let's analyze the image:

- **\(\angle PQS\)** seems to be approximately 65 degrees based on its placement relative to the protractor.
- **\(\angle RQS\)** appears to be around 35 degrees.

Now we calculate the sum:

\[
m\angle PQS + m\angle RQS = 65^\circ + 35^\circ = 100^\circ
\]

Thus:
- \( m\angle PQS = 65^\circ \)
- \( m\angle RQS = 35^\circ \)
- \( m\angle PQS + m\angle RQS = 100^\circ \)

Let me know if you'd like further explanation or have additional questions!

### Related Questions:
1. How do you use a protractor for angle measurement?
2. What is the definition of adjacent angles?
3. What is the sum of angles around a point?
4. How can you find unknown angles in a triangle if two angles are known?
5. What are complementary and supplementary angles?

**Tip:** Always ensure the base line of the protractor is aligned correctly with one of the arms of the angle for accurate measurements.

Given \(\overline{PQR}\), use the protractor to measure \(\angle PQS\) and \(\angle RQS\). Also determine the sum of two angle measurements.

Learn how to measure angles \(\angle PQS\) and \(\angle RQS\) using a protractor. This problem involves using the protractor to find angle measurements and calculating the sum of these angles, suitable for students in Grades 6-8.

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