https://file.aiquickdraw.com/mathbot/file/1727876750991ma04szyw.jpg

Let's analyze the diagram and the problem presented.

We are given two angles:
- One is labeled as \((5x + 8)^\circ\),
- The other is \((26 + 2x)^\circ\).

These angles seem to be alternate interior angles, which means they must be equal if lines \(m\) and \(n\) are parallel. To find the value of \(x\) that makes the lines parallel, we can set the expressions for the two angles equal to each other and solve for \(x\):

\[
(5x + 8)^\circ = (26 + 2x)^\circ
\]

### Steps to solve for \(x\):

1. Subtract \(2x\) from both sides:
   \[
   5x - 2x + 8 = 26
   \]
   \[
   3x + 8 = 26
   \]

2. Subtract 8 from both sides:
   \[
   3x = 18
   \]

3. Divide both sides by 3:
   \[
   x = 6
   \]

Now that we have \(x = 6\), we can substitute it back into the angle expressions to verify that the angles are indeed equal:

- \((5x + 8)^\circ = 5(6) + 8 = 30 + 8 = 38^\circ\),
- \((26 + 2x)^\circ = 26 + 2(6) = 26 + 12 = 38^\circ\).

Both angles are equal to \(38^\circ\), which confirms that lines \(m\) and \(n\) are parallel.

Thus, the measure of angle 1 that makes lines \(m\) and \(n\) parallel is \(38^\circ\).

---

Would you like more details on any step, or do you have further questions?

Here are 5 additional related questions you can explore:
1. What are alternate interior angles, and why do they ensure parallel lines?
2. How can the concept of corresponding angles help in proving parallel lines?
3. What other properties of angles can be used to identify parallel lines?
4. How do transversal lines affect the angles formed by intersecting lines?
5. How would the problem change if the lines were not parallel?

**Tip:** In geometry, always look for pairs of congruent angles (alternate interior, corresponding, etc.) to quickly assess whether lines are parallel.

The user is presented with a diagram showing two lines m and n intersected by a transversal, with angles (5x + 8)° and (26 + 2x)° marked. The task is to find the value of angle 1 that makes lines m and n parallel.

Learn how to solve a geometry problem involving parallel lines and alternate interior angles. Given angles (5x + 8)° and (26 + 2x)°, find the value of x and confirm that the lines are parallel. Suitable for Grades 7-9.

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