https://file.aiquickdraw.com/mathbot/file/17260103904591jkwnnvn.jpg

Let's go through the questions shown in the image:

1. **Question 7:** "Two lines cut by a transversal are parallel if the alternate exterior angles formed are ___."
   - The answer should be **congruent**. When two parallel lines are cut by a transversal, the alternate exterior angles are equal in measure.

2. **Question 8:** "What is the value of \(x\)? Show your work."
   - From the diagram provided, the two angles involved are \(3x^\circ\) and \(87^\circ\), which are alternate exterior angles. For the lines to be parallel, these angles must be congruent.
   - Set up the equation: 
     \[
     3x = 87
     \]
   - Solving for \(x\):
     \[
     x = \frac{87}{3} = 29
     \]
   - So, the value of \(x\) is **29**.

Would you like further clarification or details? Here are 5 related questions to deepen your understanding:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How can you use the corresponding angles postulate to prove lines are parallel?
3. Can the same approach be used to find angles if the lines are not parallel?
4. Why is it important for transversal lines to form specific angle relationships for proving parallelism?
5. What would the equation look like if the angles formed were not congruent?

**Tip:** Remember, when dealing with parallel lines and a transversal, various angle relationships (like corresponding, alternate interior, and alternate exterior angles) help determine line properties.

Two lines cut by a transversal are parallel if the alternate exterior angles formed are ___. What is the value of x? Show your work.

Learn how to solve for x using the Alternate Exterior Angles Theorem in a transversal setup. In this problem, two parallel lines are cut by a transversal, and the angles formed are used to find the value of x. This is a core concept in Geometry, perfect for students in Grades 7-9.

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