Given that line $k$ is parallel to line $l$, and a transversal intersects both lines forming angle $1$ on line $k$, which angle on line $l$ is congruent to angle $1$?

• A. The adjacent angle to angle $1$ on line $k$
• B. The alternate interior angle on line $k$
• C. The corresponding angle formed on line $l$ by the transversal
• D. The vertical angle to angle $1$ on line $k$

Answer: (C)

Verified step by step guidance

1. Identify the given elements: two parallel lines \( k \) and \( l \), and a transversal intersecting both lines, creating angle 1 on line \( k \).
2. Recall the types of angles formed when a transversal crosses parallel lines: corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
3. Understand that corresponding angles are pairs of angles that are in the same relative position at each intersection where the transversal crosses the parallel lines.
4. Recognize that angle 1 on line \( k \) has a corresponding angle on line \( l \) which is congruent to angle 1 due to the Parallel Postulate and the Corresponding Angles Postulate.
5. Conclude that the angle congruent to angle 1 on line \( l \) is the corresponding angle formed by the transversal, not the adjacent angle, alternate interior angle on the same line, or the vertical angle on line \( k \).