To solve the equation ctg(π/4 - x) = 1, we can rewrite it in terms of cotangent:

cot(π/4 - x) = 1

Next, we know that cotangent is the reciprocal of tangent, so we can rewrite the equation in terms of tangent:

tan(π/4 - x) = 1

Now, we can use the trigonometric identity tan(π/4 - x) = tan(π/4 + x) to simplify the equation:

tan(π/4 + x) = 1

Since tan(π/4) = 1, we can rewrite the equation as:

tan(x) = 1

This means that the angle x is equal to π/4, or 45 degrees.