To find the values of $m$ and $y$ in the given diagram, we can use the properties of parallel lines and the angles formed by a transversal.

Step 1: Identify the relationships between angles

• The angle given as $140^\circ$ is an exterior angle.
• The angle $m$ and $140^\circ$ are alternate interior angles because the lines are parallel, so they are equal.

Thus: $m = 140^\circ$

Step 2: Determine the relationship involving $y$

• The angle $2y$ is vertically opposite to angle $m$, so: $2y = m$ Substitute $m = 140^\circ$ from Step 1: $2y = 140^\circ$

Step 3: Solve for $y$

To find $y$: $y = \frac{140^\circ}{2} = 70^\circ$

Final Values:

• $m = 140^\circ$
• $y = 70^\circ$

Would you like a more detailed explanation of these steps or have any questions? Here are some related questions to deepen your understanding:

1. What are the properties of alternate interior angles?
2. How do vertically opposite angles help in solving problems involving parallel lines?
3. Can you explain why the sum of angles around a point is 360°?
4. How would the problem change if the lines were not parallel?
5. What other angle pairs are equal when a transversal cuts parallel lines?

Tip: When working with angles formed by a transversal across parallel lines, remember that alternate interior angles are always equal.