Angles x/3 and x-20 are co-interior angles formed by parallel lines AB and DC intersected by transversal FY. Find the value of x.

let's tackle this geometry problem!

1.1.1

Step 1: Identify the parallel lines and transversal.
Lines AB and DC are parallel. The vertical line passing through F and Y is a transversal.

Step 2: Identify the relationship between the angles $x/3$ and $x-20^\circ$.
The angle $\angle AFY = \frac{x}{3}$ and the angle $\angle FYD = x-20^\circ$ are co-interior angles.

Step 3: Set up the equation and solve for $x$.
Co-interior angles between parallel lines are supplementary (sum to $180^\circ$).

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