This diagram shows two sets of parallel lines: $a \parallel b$ and $c \parallel d$, with a perpendicular line intersecting at different points marked with angles and segments. You're also given specific angle measures: $\text{m} \angle 3 = 52^\circ$ and $\text{m} \angle 21 = 100^\circ$.

Would you like assistance solving for certain angles or explaining the relationships between the lines and angles in this image? Let me know if you have a specific problem in mind, and I can help break it down step by step.

Here are 5 questions that could expand on this information:

1. How do we calculate the remaining angles in the diagram using parallel line and transversal angle rules?
2. What are alternate interior and corresponding angles in this setup?
3. How do we apply the perpendicularity condition to find unknown angles?
4. How can we use supplementary angles to solve for others in the diagram?
5. What role does the given $\text{m} \angle 3 = 52^\circ$ and $\text{m} \angle 21 = 100^\circ$ play in determining other angles?

Tip: In diagrams involving parallel lines and transversals, corresponding and alternate interior angles are equal.