To find the values of $m$ and $y$ in the given image, we can use the properties of angles in parallel lines and transversals.

Analyzing the Image:

1. Angles and Parallel Lines:

   • The angle marked $140^\circ$ is an exterior angle formed by the transversal with the lower parallel line.
   • The angle $m$ is an interior angle on the opposite side of the transversal.
   • The angle $2y$ is on the opposite side of angle $m$, suggesting it may be an alternate interior angle.

2. Using Alternate Interior Angles:

   • For alternate interior angles, $m$ and $140^\circ$ should be equal. $m = 140^\circ$

3. Using Linear Pair Property:

   • The angle $2y$ and $140^\circ$ are supplementary because they form a linear pair on the straight line. $2y + 140^\circ = 180^\circ$ $2y = 180^\circ - 140^\circ$ $2y = 40^\circ$ $y = 20^\circ$

Summary:

• The value of $m$ is $140^\circ$.
• The value of $y$ is $20^\circ$.

Would you like further explanations or have any additional questions?

Related Questions:

1. What are alternate interior angles and how are they determined?
2. How do corresponding angles in parallel lines compare?
3. What is the sum of the interior angles in any polygon?
4. How can you determine angles formed by intersecting lines?
5. What is the significance of the transversal line in parallel line geometry?

Tip: Always remember that alternate interior angles are equal when two lines are parallel and are cut by a transversal.