The problem involves two parallel lines, A and B, with a transversal line C cutting across them. We are asked to find the value of $x$, using angle relationships.

Here’s the setup:

• The angle on line A is given as $7x + 25^\circ$.
• The angle formed by the transversal line C and line B is $60^\circ$.
• The two lines A and B are parallel, and line C is a transversal.

We know that when a transversal intersects two parallel lines, the corresponding angles are equal. In this case, the angle formed by line A and the transversal is a corresponding angle to the angle formed by line B and the transversal. So:

$7x + 25^\circ = 60^\circ$

Now, let's solve for $x$:

1. Subtract 25 from both sides: $7x = 60^\circ - 25^\circ$ $7x = 35^\circ$

2. Divide both sides by 7: $x = \frac{35^\circ}{7} = 5$

Thus, the value of $x$ is 5.

Would you like further details or have any questions on the solution?

Here are some related questions for further practice:

1. What other angle relationships can be used with parallel lines and transversals?
2. How would the solution change if the lines were not parallel?
3. Can you identify other types of angle pairs formed by a transversal cutting parallel lines?
4. What are alternate interior angles, and how do they relate to this problem?
5. How can you apply this concept in real-world scenarios?

Tip: When working with parallel lines and a transversal, always look for corresponding, alternate interior, and alternate exterior angles to set up equations.