To find the angle between two lines, we need to find the direction vectors of both lines and then use the dot product formula.

First, let's find the direction vector of the line in which the plane 3x - 7y - 5z = 1 cuts the plane 8x - 11y - 3z = 0.

To find the direction vector of this line, we can find two points on the line and subtract their coordinates.

Let's choose two arbitrary values for x and solve the equations to find corresponding values of y and z:

For x = 0:
3(0) - 7y - 5z = 1
-7y - 5z = 1

Let's choose y = 0 and solve for z:
-5z = 1
z = -1/5

So one point on the line is (0, 0, -1/5).

For x = 1:
3(1) - 7y - 5z = 1
-7y - 5z = -2

Let's choose y = 0 and solve for z:
-5z = -2
z = 2/5

So another point on the line is (1, 0, 2/5).

Now let's find the direction vector by subtracting the coordinates of the two points:

(1, 0, 2/5) - (0, 0, -1/5) = (1, 0, 3/5)

So the direction vector of the line in which the plane 3x - 7y - 5z = 1 cuts the plane 8x - 11y - 3z = 0 is (1, 0, 3/5).

Now let's find the direction vector of the line in which the plane 5x - 13y + 3x + 2 = 0 cuts the plane 8x - 11y - 3z = 0.

To find the direction vector of this line, we can find two points on the line and subtract their coordinates.

Let's choose two arbitrary values for x and solve the equations to find corresponding values of y and z:

For x = 0:
5(0) - 13y + 3x + 2 = 0
-13y + 2 = 0

Let's choose y = 0 and solve for z:
-13(0) + 2 = 0
2 = 0

This is a contradiction, so there are no points on this line.

Therefore, the angle between the lines is undefined.