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°).