b We know that ∠ w and ∠ k make a linear pair, which means they are supplementary angles. If these angles are equal, then we know that each of them must be a right angle. With this information we know that n and m are perpendicular lines. Note that this does not necessarily tell us that l and m are parallel.
The fact that ∠ r and ∠ q are congruent does not tell us anything about the relationship between the lines.
d To relate ∠ z and ∠ k, we first recognize that ∠ z and ∠ h are corresponding angles and ∠ h and ∠ k form a linear pair, meaning they are supplementary angles.
The corresponding angles would be congruent if l∥ m. If that was the case, ∠ z and ∠ k would also be supplementary angles. However, since we have z+k=160^(∘), we know that ∠ z and ∠ k are not supplementary, which means l and m cannot be parallel lines.
