Find the values of x and y in the diagram.

The angle $x$ and the $92^\circ$ angle form a linear pair on a straight line. Angles on a straight line sum to $180^\circ$.

$$x + 92^\circ = 180^\circ$$ $$x = 180^\circ - 92^\circ$$ $$x = 88^\circ$$

The sum of the interior angles in a triangle is $180^\circ$. The three interior angles are $41^\circ$, $y$, and $x$.

$$41^\circ + y + x = 180^\circ$$

Substitute the value of $x$ found in Step 1:

$$41^\circ + y + 88^\circ = 180^\circ$$ $$129^\circ + y = 180^\circ$$ $$y = 180^\circ - 129^\circ$$ $$y = 51^\circ$$

The values are:
$x = \boxed{\text{88}^\circ}$
$y = \boxed{\text{51}^\circ}$