Use formula tanx =[(m1-m2)/(1+m1×m2)]

m1=-a/b and m2= (a+b)/(a-b)

Given:
- Two lines: ax + by + c = 0 and (a/b)x = (a/b)y
- a, b are non-zero real numbers

To find:
- The acute angle between the given lines

Solution:
The equation of a line in slope-intercept form is y = mx + c, where m is the slope of the line and c is the y-intercept. Comparing this form with the given equations, we can rewrite them as:

1. Equation 1: y = -(a/b)x - c/b
2. Equation 2: y = (a/b)x

The slopes of the two lines can be obtained by comparing the coefficients of x in the equations:

1. Slope of Line 1 (m1) = -(a/b)
2. Slope of Line 2 (m2) = a/b

The acute angle between two lines is given by the formula:

θ = tan^(-1) |(m2 - m1) / (1 + m1 * m2)|

Calculating the acute angle:

1. Substitute the values of m1 and m2 in the formula:
θ = tan^(-1) |(a/b + a/b) / (1 + -(a/b) * (a/b))|

2. Simplify the expression:
θ = tan^(-1) |(2a/b) / (1 + (a/b)^2)|

3. Use the property of absolute value:
θ = tan^(-1)(2a/b) / (1 + (a/b)^2) (since a/b is positive)

4. Substitute a/b with a single variable (k) for simplicity:
θ = tan^(-1)(2k) / (1 + k^2)

5. The acute angle is independent of a and b, so we can choose any non-zero real number for a/b.
Let's choose k = 1 for simplicity.

6. Substitute k = 1 in the equation:
θ = tan^(-1)(2) / (1 + 1^2)
= tan^(-1)(2) / 2

7. Evaluate the expression using a calculator:
θ ≈ 26.57°

Conclusion:
The acute angle between the given lines is approximately 26.57°, which corresponds to option A.