The problem asks to find the values of $x$ and $y$ in the given figure, where three parallel lines are intersected by a transversal. The angles are given as $4x^\circ$, $56^\circ$, and $(3y-11)^\circ$.

1. Problem Description

The problem asks to find the values of $x$ and $y$ in the given figure, where three parallel lines are intersected by a transversal. The angles are given as $4x^\circ$, $56^\circ$, and $(3y-11)^\circ$.

2. Solution Steps

Since the lines are parallel, corresponding angles are equal.

Therefore, $4x = 56$.

Divide both sides by 4:

$x = \frac{56}{4} = 14$

Also, the angle $(3y - 11)^\circ$ corresponds to the $56^\circ$ angle.

Thus, $3y - 11 = 56$.

Add 11 to both sides:

$3y = 56 + 11$

$3y = 67$

Divide both sides by 3:

$y = \frac{67}{3}$

3. Final Answer

$x = 14$

$y = \frac{67}{3}$