https://file.aiquickdraw.com/mathbot/file/172618586474985evb8n5.jpg

The image shows a geometric diagram with several lines and points labeled, along with a question asking to "select all the pairs of adjacent angles." 

Here are the pairs listed:

1. ∠STV and ∠STQ
2. ∠RQO and ∠RQT
3. ∠PQO and ∠PQT
4. ∠RQT and ∠PQT

### Explanation:

Adjacent angles are two angles that share a common vertex and a common side but do not overlap. Let’s go through each option:

1. **∠STV and ∠STQ**:
   - These angles share the common side **ST** and the common vertex **T**. Therefore, this pair is **adjacent**.

2. **∠RQO and ∠RQT**:
   - These angles share the common side **RQ** and the common vertex **Q**. Hence, this pair is **adjacent**.

3. **∠PQO and ∠PQT**:
   - These angles share the common side **PQ** and the common vertex **Q**. Therefore, this pair is **adjacent**.

4. **∠RQT and ∠PQT**:
   - These angles also share the common vertex **Q** but do **not** share a common side, as they are opposite angles. So, this pair is **not adjacent**.

### Correct Selections:
- ∠STV and ∠STQ (Correct)
- ∠RQO and ∠RQT (Correct)
- ∠PQO and ∠PQT (Correct)
- ∠RQT and ∠PQT (Incorrect)

Let me know if you need further details!

### Related questions:
1. What is the difference between adjacent and vertical angles?
2. Can adjacent angles be supplementary or complementary?
3. How do you calculate the measure of adjacent angles if one angle is known?
4. What role do adjacent angles play in geometric proofs?
5. Are adjacent angles always formed by intersecting lines?

### Tip:
Adjacent angles are often used in various geometric theorems, such as the linear pair theorem, which states that adjacent angles formed by intersecting lines are supplementary (sum to 180°).

Learn how to identify pairs of adjacent angles in a geometric diagram. This problem covers the concept of adjacent angles, their properties, and how to apply the Adjacent Angles Theorem and Linear Pair Theorem. Suitable for students in Grades 6-8.

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