Given:
Lines: x = 5 and √3x - y + 6 = 0

To Find:
The angle between the given lines.

Solution:

Step 1: Find the slopes of the lines
The given line x = 5 is a vertical line parallel to the y-axis. The slope of a vertical line is undefined.

The second line √3x - y + 6 = 0 can be rewritten as:
y = √3x + 6

Comparing it with the slope-intercept form y = mx + c, we can see that the slope of this line is √3.

Step 2: Find the angle between the lines
The angle between two lines is given by the formula:
θ = arctan((m2 - m1) / (1 + m1 * m2))

Let's substitute the values of slopes m1 = undefined and m2 = √3 into the formula:

θ = arctan((√3 - undefined) / (1 + undefined * √3))

Since the slope of the first line is undefined, the denominator in the formula becomes 0. Therefore, the angle between the lines is also undefined.

Conclusion:
The angle between the lines x = 5 and √3x - y + 6 = 0 is undefined.

Re-write the question again.