Let's analyze the given diagram and verify the statements based on the angle relationships.

1. $x^\circ = w^\circ$ because they are alternate interior angles.

   • True. $x^\circ$ and $w^\circ$ are alternate interior angles as they lie between two parallel lines on opposite sides of the transversal.

2. $v^\circ = y^\circ$ because they are alternate interior angles.

   • True. $v^\circ$ and $y^\circ$ are also alternate interior angles as they lie between two parallel lines on opposite sides of the transversal.

3. $v^\circ + y^\circ = 180^\circ$ because they are supplementary angles.

   • False. $v^\circ$ and $y^\circ$ are not on the same straight line; they are alternate interior angles, not supplementary angles.

4. $x^\circ + y^\circ = 180^\circ$ because they are corresponding angles.

   • False. $x^\circ$ and $y^\circ$ are not corresponding angles. Corresponding angles lie on the same side of the transversal, but $x^\circ$ and $y^\circ$ are not positioned in such a way.

5. $v^\circ = w^\circ$ because they are corresponding angles.

   • True. $v^\circ$ and $w^\circ$ are corresponding angles since they lie on the same side of the transversal and in matching positions.

6. $x^\circ + y^\circ = 180^\circ$ because they are supplementary angles.

   • True. $x^\circ$ and $y^\circ$ are supplementary angles because they are on the same straight line formed by the transversal cutting through the parallel lines.

True Statements:

• $x^\circ = w^\circ$ because they are alternate interior angles.
• $v^\circ = y^\circ$ because they are alternate interior angles.
• $v^\circ = w^\circ$ because they are corresponding angles.
• $x^\circ + y^\circ = 180^\circ$ because they are supplementary angles.

Do you want further details on any of the statements or clarifications?

Here are 5 related questions:

1. How can you identify corresponding angles in a transversal?
2. What is the relationship between alternate exterior angles?
3. Can vertically opposite angles also be supplementary?
4. How do we prove that two lines are parallel using angles?
5. What is the sum of the interior angles in any polygon?

Tip: When two parallel lines are cut by a transversal, alternate interior and corresponding angles are always equal.