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The image shows two parallel lines \( m \parallel n \), and there are two angles labeled as \( (x-2)^\circ \) and \( (x-14)^\circ \). Since the lines are parallel, the angles shown are corresponding angles. According to the Corresponding Angles Postulate, corresponding angles are congruent when two parallel lines are cut by a transversal.

This gives us the equation:

\[
(x - 2)^\circ = (x - 14)^\circ
\]

### Solving the equation:

1. Start with the equation:
   \[
   x - 2 = x - 14
   \]

2. Subtract \( x \) from both sides:
   \[
   -2 = -14
   \]

3. This results in a contradiction. Therefore, I made an error in interpreting the angles.

Let me try again.

**Since the angles are supplementary (add up to 180°):**

\[
(x - 2) + (x - 14) = 180^\circ
\]

### Solving for \( x \):

1. Simplify the left-hand side:
   \[
   2x - 16 = 180
   \]

2. Add 16 to both sides:
   \[
   2x = 196
   \]

3. Divide by 2:
   \[
   x = 98
   \]

So, the value of \( x \) is \( \boxed{98} \).

Would you like more details or have any questions about this solution? 

Here are five related questions to explore further:
1. How do corresponding angles behave with parallel lines?
2. What are alternate interior angles, and how do they relate to parallel lines?
3. Can angles on the same side of a transversal ever be congruent?
4. How do we know when angles are supplementary in parallel line problems?
5. How would this problem change if the lines weren't parallel?

**Tip:** When dealing with parallel lines, always consider whether the angles are congruent or supplementary depending on their positions (corresponding, alternate, etc.).

Given m || n, find the value of x. The angles are labeled (x - 2)° and (x - 14)°.

Learn how to find the value of x in a problem involving parallel lines and angles using the Supplementary Angles Theorem. The problem includes angles (x - 2)° and (x - 14)° which sum up to 180°. Suitable for students in Grades 7-9.

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