In the given diagram, line $c$ intersects two parallel lines $s$ and $t$. The angle labeled $110^\circ$ is formed between line $c$ and line $t$. We are tasked with finding the value of angle $x$.

Step-by-step Solution:

1. Identify Corresponding Angles: The two lines $s$ and $t$ are parallel, and line $c$ acts as a transversal. This means that the angles formed by the transversal with the two parallel lines are related. In this case, the angle of $110^\circ$ with line $t$ is adjacent to the angle $x$ on line $s$.

2. Use Supplementary Angles: Since the angle between line $c$ and line $t$ is $110^\circ$, the adjacent angle on the same side of line $c$ (on line $s$) is supplementary to this $110^\circ$ angle. The supplementary angles sum to $180^\circ$.

   $110^\circ + x = 180^\circ$

3. Solve for $x$: $x = 180^\circ - 110^\circ = 70^\circ$

Thus, the value of $x$ is $70^\circ$.

Do you have any questions or need further clarification on this problem?

Related Questions:

1. How do we identify corresponding angles in a transversal with parallel lines?
2. What is the difference between supplementary and complementary angles?
3. How can we use alternate interior angles to solve problems involving parallel lines?
4. Can you solve a similar problem where the transversal forms different angles?
5. How would you solve for angles when there are multiple transversals?

Tip:

When working with parallel lines and a transversal, always remember that alternate interior angles and corresponding angles are equal, and adjacent angles on a straight line are supplementary.