Let's analyze the geometry problem shown in the image.

Part a: Name a pair of perpendicular lines

Perpendicular lines intersect at a 90° angle. Looking at the diagram, we can see that the lines $PQ$ and $YZ$ meet at point $Z$ and form a right angle, indicated by the small square near $Z$. Thus, the pair of perpendicular lines is:

• $PQ$ and $YZ$

Part b: Determine the value of $q$

The diagram shows multiple lines intersecting at various angles, and $q$ seems to represent certain angles at the intersection of lines, specifically at point $W$. To solve for $q$, we would need additional information such as relationships between angles (e.g., if angles are complementary or supplementary).

Do you have more details for part b, or should I make assumptions based on standard angle properties?

Would you like any further explanation or clarification? Here are five related questions for deeper understanding:

1. How do we determine if two lines are perpendicular from a diagram without angle measures?
2. What are complementary and supplementary angles, and how do they apply in this scenario?
3. How can we find unknown angles when lines intersect?
4. What properties of parallel and perpendicular lines are useful in geometry problems?
5. What role do right angles play in determining perpendicularity?

Tip: When solving geometry problems involving angles, always look for clues like right-angle markers and use known angle relationships like complementary (sum = 90°) and supplementary (sum = 180°) angles.