Geometry

Question Analysis

This question involves identifying the relationships of different angle pairs. The main focus is on understanding the properties of parallel lines cut by a transversal.

Key Concept Explanation:

When two parallel lines are cut by a transversal, several angle relationships hold true:

Corresponding angles are congruent.

Alternate interior angles are congruent.

Same-side interior angles are supplementary (add up to 180°).

Vertical angles are always congruent.

Option Analysis

The angle pairs not congruent is Option C, because same-side interior angles are supplementary for parallel lines cut by a transversal (not congruent).

The other options are congruent:

Option A: Vertical angles (formed by intersecting lines) are always congruent, regardless of whether the intersecting lines are parallel or not.