To solve the equation sin(2x-20°) = cos(x), we can use the trigonometric identity sin(90° - θ) = cos(θ).

First, let's rewrite the equation using this identity:
sin(90° - (2x - 20°)) = cos(x)

Next, simplify the expression inside the sine function:
sin(90° - 2x + 20°) = cos(x)

Combine like terms:
sin(110° - 2x) = cos(x)

Now, we can use the identity sin(θ) = cos(90° - θ) to rewrite the equation:
cos(90° - (110° - 2x)) = cos(x)

Simplify the expression inside the cosine function:
cos(90° - 110° + 2x) = cos(x)

Combine like terms:
cos(-20° + 2x) = cos(x)

Since the cosine function is an even function, we can rewrite the equation as:
cos(20° - 2x) = cos(x)

Now, we can equate the angles inside the cosine function:
20° - 2x = x

Solve for x:
20° = 3x
x = 20°/3

Therefore, the solution to the equation sin(2x-20°) = cos(x) is x = 20°/3.