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The image presents a problem involving parallel lines \( m \parallel n \) and a transversal \( t \), with two given angles expressed as \( (8x + 6)^\circ \) and \( (4x + 30)^\circ \).

Since lines \( m \) and \( n \) are parallel, the two angles are either alternate interior angles, corresponding angles, or supplementary angles. Observing the position, these angles are **alternate interior angles**, which are **equal** when the lines are parallel.

Therefore, we can set the two expressions equal to each other:

\[
8x + 6 = 4x + 30
\]

### Solving for \( x \):

1. Subtract \( 4x \) from both sides:
   \[
   8x - 4x + 6 = 30
   \]
   \[
   4x + 6 = 30
   \]

2. Subtract 6 from both sides:
   \[
   4x = 24
   \]

3. Divide both sides by 4:
   \[
   x = 6
   \]

So, the value of \( x \) is **6**.

### Angle Pair Relationship:
The angle pair relationship is **alternate interior angles**.

Would you like more details or further explanations?

### Here are 5 related questions:
1. What are alternate exterior angles, and how do they relate to parallel lines?
2. How do corresponding angles behave when a transversal crosses parallel lines?
3. What would happen if the lines weren't parallel in this scenario?
4. Can you solve for the actual measure of the angles once \( x \) is known?
5. How would you solve if the angles were supplementary instead of congruent?

#### Tip:
In geometry, understanding how different types of angles behave with parallel lines and transversals is key to solving many angle-related problems.

Given m||n, find the value of x. State the angle pair relationship. The two angles are (8x + 6)° and (4x + 30)°.

Learn how to solve for x in a geometry problem involving parallel lines and a transversal. The angles given are (8x + 6)° and (4x + 30)°. By applying the Alternate Interior Angle Theorem, find the value of x and understand the angle pair relationship.

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