Solve both parts and justify the conditions used. Part A: A line l is outside plane α and parallel to a line m in α. State and justify the conclusion. Part B: How many vertices does an 10-gonal prism have?

1. Part A reasoning

2. Apply a parallelism criterion with all its incidence and outside-plane conditions.

3. Calculate or simplify this relation.

   $$l\parallel m\subseteq\alpha,\ l\not\subseteq\alpha\Rightarrow l\parallel\alpha$$

4. Without the outside-plane condition, l could be contained in α.

5. Part B reasoning

6. Identify the defining faces, cross-sections and generating elements of the solid.

7. Calculate or simplify this relation.

   $$V=2n=2(10)=20$$

8. Corresponding base vertices are distinct and joined by lateral edges.

A: l is parallel to α. B: The requested value is 20.

Checks and common pitfalls: Without the outside-plane condition, l could be contained in α. Corresponding base vertices are distinct and joined by lateral edges.