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The problem involves two parallel lines with a transversal intersecting them, forming angles marked as \( (2x - 29)^\circ \) and \( (x + 5)^\circ \). We are asked to find the measure of each marked angle, assuming the lines are parallel.

In situations where a transversal intersects two parallel lines, corresponding angles are equal. Therefore, we can set the two angles equal to each other:

\[
2x - 29 = x + 5
\]

### Step-by-step solution:
1. Subtract \( x \) from both sides to isolate \( x \) on one side:
   \[
   2x - x - 29 = 5
   \]
   Simplifying this, we get:
   \[
   x - 29 = 5
   \]

2. Add 29 to both sides to solve for \( x \):
   \[
   x = 34
   \]

Now that we have the value of \( x \), we can substitute it back into both expressions for the angles:

- The first angle is \( 2x - 29 \):
  \[
  2(34) - 29 = 68 - 29 = 39^\circ
  \]

- The second angle is \( x + 5 \):
  \[
  34 + 5 = 39^\circ
  \]

Thus, both angles measure \( 39^\circ \), which is consistent since corresponding angles should be equal.

### Final Answer:
Both marked angles measure \( 39^\circ \).

Would you like further details or clarification on this solution?

Here are 5 related questions to expand your understanding:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. How would you solve for \( x \) if the angles were alternate exterior angles?
3. What happens to the angles if the lines are not parallel?
4. Can corresponding angles be supplementary? Under what conditions?
5. What is the relationship between consecutive interior angles and parallel lines?

**Tip**: Always look for angle relationships like corresponding, alternate, and consecutive interior when dealing with parallel lines and a transversal!

Find the measure of each marked angle. Assume the lines are parallel. (2x - 29)° and (x + 5)°

This problem involves finding the measures of angles formed by a transversal intersecting two parallel lines. Using the Corresponding Angles Postulate, we set the angles (2x - 29)° and (x + 5)° equal to solve for x, resulting in equal angle measures. Suitable for Grades 7-10.

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