This problem involves parallel lines cut by a transversal, creating angles. In the image, you have two parallel lines and a transversal, and we are asked to find the value of $x^\circ$.

Given that one of the angles is $140^\circ$, we can use the fact that corresponding angles formed by a transversal cutting through parallel lines are congruent (equal). Additionally, angles on the same side of the transversal (interior angles) sum up to $180^\circ$.

Solution:

• The angle marked $x^\circ$ and the angle of $140^\circ$ are on the same side of the transversal, forming a pair of interior angles.
• Therefore, they must be supplementary. That is: $x + 140^\circ = 180^\circ$
• Solving for $x$: $x = 180^\circ - 140^\circ = 40^\circ$

Thus, $x = 40^\circ$.

Would you like further details or have any questions?

Related Questions:

1. What are alternate interior angles, and how are they used to solve angle problems?
2. How do corresponding angles relate when two parallel lines are cut by a transversal?
3. Can you explain the difference between supplementary and complementary angles?
4. What other angle relationships exist when a transversal crosses parallel lines?
5. How do you solve for unknown angles in complex geometric figures?

Tip:

When dealing with parallel lines and a transversal, always remember that alternate interior, corresponding, and co-interior angles follow specific patterns and relationships that simplify solving for unknown angles.