From the image you've uploaded, we can identify various types of angle pairs within the given geometric figure:

1. Vertically Opposite Angles:

   • Angles $P$ and $Q$ are vertically opposite angles.
   • Angles $R$ and $S$ are also vertically opposite angles.

2. Adjacent Complementary Angles:

   • It is indicated in the diagram that angle $R$ is twice angle $Q$. Assuming $R$ and $Q$ add up to $90^\circ$ (since this is not explicitly stated, it’s a hypothesis based on the common interpretation of complementary angles in geometry), these angles are complementary.
   • Therefore, angles $R$ and $Q$ are adjacent complementary angles.

3. Linear Pair:

   • Angles $S$ and $Q$ form a linear pair as they are adjacent and their non-common arms are on the same line, typically summing up to $180^\circ$.

4. Adjacent Angles That Do Not Form a Linear Pair:

   • Angles $P$ and $S$ are adjacent but do not form a linear pair as their sum does not amount to $180^\circ$, assuming from the geometric arrangement in the diagram.

Would you like more details on any of these points, or do you have other questions about this figure?

Here are some relative questions to expand your understanding:

1. How can we prove that angles $R$ and $Q$ are actually complementary?
2. What are the properties of vertically opposite angles?
3. How do we find the measure of angles $P$, $Q$, $R$, and $S$ if one of them is known?
4. What is the significance of a linear pair in geometric proofs?
5. Can angles that are not adjacent ever be complementary or supplementary?

Tip: When analyzing geometric figures, always check if additional conditions like parallel lines or symmetry might influence the angle relationships.