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The problem is in Mongolian and can be translated as follows:

We are given the equation of a line:
\[
y = (2a - 3)x + 2
\]

This line is supposed to be perpendicular to the line that passes through points \( A(-2, 6) \) and \( B(2, -2) \). We are asked to find the angle \( \theta \) of line \( n \).

### Solution Steps:

1. **Find the Slope of Line \( AB \):**
   The slope \( m_{AB} \) of the line passing through points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) can be found using the formula:
   \[
   m_{AB} = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting \( A(-2, 6) \) and \( B(2, -2) \):
   \[
   m_{AB} = \frac{-2 - 6}{2 - (-2)} = \frac{-8}{4} = -2
   \]

2. **Determine the Slope of the Perpendicular Line:**
   Since the line given in the equation is perpendicular to \( AB \), its slope \( m \) should satisfy:
   \[
   m \cdot m_{AB} = -1
   \]
   Substituting \( m_{AB} = -2 \):
   \[
   m \cdot (-2) = -1 \Rightarrow m = \frac{1}{2}
   \]

3. **Set the Slope of the Given Line Equal to \( \frac{1}{2} \):**
   The slope of the line \( y = (2a - 3)x + 2 \) is \( 2a - 3 \). Set this equal to \( \frac{1}{2} \) to solve for \( a \):
   \[
   2a - 3 = \frac{1}{2}
   \]
   Solving for \( a \):
   \[
   2a = \frac{1}{2} + 3 = \frac{1}{2} + \frac{6}{2} = \frac{7}{2}
   \]
   \[
   a = \frac{7}{4}
   \]

4. **Find the Angle \( \theta \):**
   The angle \( \theta \) that the line makes with the positive \( x \)-axis can be found using the slope \( m = \frac{1}{2} \):
   \[
   \theta = \tan^{-1} \left(\frac{1}{2}\right)
   \]

Using this information, we can conclude:
1. \( a = \frac{7}{4} \).
2. \( \theta = \tan^{-1}\left(\frac{1}{2}\right) \), which can be calculated for an approximate value if needed.

Would you like the approximate value for \( \theta \), or have any questions about the steps?

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### Further Related Questions:

1. How would the solution change if the line wasn't perpendicular to \( AB \)?
2. What is the formula for finding the angle between two intersecting lines?
3. Can you find the equation of the line passing through \( A \) and \( B \)?
4. How does the slope of a line relate to its angle with the x-axis?
5. How can you verify if two lines are perpendicular just by looking at their slopes?

### Tip:
For perpendicular lines, the product of their slopes is always \(-1\). This rule is essential in coordinate geometry.

y = (2a - 3)x + 2 шугам нь A(-2,6) ба B(2,-2) цэгийг дайрсан шугамтай перпендикуляр бол n-ийн өнцгийг ол.

Learn how to solve the problem of finding the angle between a given line and another perpendicular line passing through points A(-2, 6) and B(2, -2). This problem covers key concepts in coordinate geometry, including slope calculations, perpendicular line relationships, and angle determination.

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