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The problem asks to calculate the angle between two lines given by the equations:

1. \(\frac{-2x}{2} = \frac{y+5}{-3}\)
2. \(y = 4x\) and \(y = 2 - 5x\)

### Step 1: Simplify the equations of the lines.

#### Line 1:
Given equation:
\[
\frac{-2x}{2} = \frac{y + 5}{-3}
\]
This simplifies to:
\[
-x = \frac{y + 5}{-3}
\]
Multiply both sides by \(-3\) to get:
\[
3x = y + 5
\]
So, the equation of the first line is:
\[
y = 3x - 5
\]

#### Line 2:
We have two separate lines given by the equations:
\[
y = 4x \quad \text{and} \quad y = 2 - 5x
\]
Let's analyze the angles between each pair of lines.

### Step 2: Find the slopes of the lines.

- For \(y = 3x - 5\), the slope \(m_1 = 3\).
- For \(y = 4x\), the slope \(m_2 = 4\).
- For \(y = 2 - 5x\), the slope \(m_3 = -5\).

### Step 3: Use the formula to calculate the angle between two lines.
The angle \(\theta\) between two lines with slopes \(m_1\) and \(m_2\) is given by:
\[
\tan \theta = \left|\frac{m_1 - m_2}{1 + m_1 m_2}\right|
\]

#### Angle between Line 1 and Line 2 (\(y = 3x - 5\) and \(y = 4x\)):
\[
\tan \theta_1 = \left|\frac{3 - 4}{1 + 3 \times 4}\right| = \left|\frac{-1}{13}\right| = \frac{1}{13}
\]

So, \(\theta_1 = \arctan\left(\frac{1}{13}\right)\).

#### Angle between Line 1 and Line 3 (\(y = 3x - 5\) and \(y = 2 - 5x\)):
\[
\tan \theta_2 = \left|\frac{3 - (-5)}{1 + 3 \times (-5)}\right| = \left|\frac{8}{1 - 15}\right| = \left|\frac{8}{-14}\right| = \frac{4}{7}
\]

So, \(\theta_2 = \arctan\left(\frac{4}{7}\right)\).

### Final Answers:
- The angle between the lines \(y = 3x - 5\) and \(y = 4x\) is approximately \(\theta_1 = \arctan\left(\frac{1}{13}\right)\).
- The angle between the lines \(y = 3x - 5\) and \(y = 2 - 5x\) is approximately \(\theta_2 = \arctan\left(\frac{4}{7}\right)\).

Would you like the exact angles in degrees or radians, or any further details? 

### Related Questions:
1. How can you find the intersection point of two lines?
2. What is the geometric interpretation of the angle between two lines?
3. How does the slope of a line relate to its angle with the x-axis?
4. What is the significance of parallel lines in terms of angles?
5. How do you determine if two lines are perpendicular based on their slopes?

### Tip:
Remember that the angle between two perpendicular lines is always 90 degrees, and their slopes are negative reciprocals of each other.

Learn how to calculate the angle between two lines, specifically between y = 3x - 5 and y = 4x, using trigonometric formulas. This problem involves finding slopes, applying trigonometric identities, and understanding geometric interpretations of angles between lines.

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