The problem asks us to identify the relationship between pairs of angles formed when two parallel lines are intersected by a transversal. We need to determine the specific angle relationship and state whether the angles are congruent or supplementary. The angle pairs we need to analyze are $\angle 1$ and $\angle 3$, $\angle 2$ and $\angle 6$, and $\angle 3$ and $\angle 5$.

1. Problem Description

The problem asks us to identify the relationship between pairs of angles formed when two parallel lines are intersected by a transversal. We need to determine the specific angle relationship and state whether the angles are congruent or supplementary. The angle pairs we need to analyze are $\angle 1$ and $\angle 3$, $\angle 2$ and $\angle 6$, and $\angle 3$ and $\angle 5$.

2. Solution Steps

For $\angle 1$ and $\angle 3$:

These angles are vertical angles.

Vertical angles are congruent.

$\angle 1 \cong \angle 3$

For $\angle 2$ and $\angle 6$:

These angles are corresponding angles.

When parallel lines are cut by a transversal, corresponding angles are congruent.

$\angle 2 \cong \angle 6$

For $\angle 3$ and $\angle 5$:

These angles are alternate interior angles.

When parallel lines are cut by a transversal, alternate interior angles are congruent.

$\angle 3 \cong \angle 5$

3. Final Answer

$\angle 1$ and $\angle 3$: Vertical angles, congruent.

$\angle 2$ and $\angle 6$: Corresponding angles, congruent.

$\angle 3$ and $\angle 5$: Alternate interior angles, congruent.