Find the values of angles x and y in the diagram.

The angle $x$ and the $88^\circ$ angle form a linear pair on a straight line. Angles on a straight line sum to $180^\circ$.

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

Subtract $88^\circ$ from both sides:

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

The value of $x$ is \boxed{\text{92^\circ}}.

The sum of the interior angles in a triangle is $180^\circ$. The interior angles are $30^\circ$, $x$, and $y$.

$$30^\circ + x + y = 180^\circ$$

Substitute the value of $x = 92^\circ$ into the equation:

$$30^\circ + 92^\circ + y = 180^\circ$$ $$122^\circ + y = 180^\circ$$

Subtract $122^\circ$ from both sides:

$$y = 180^\circ - 122^\circ$$ $$y = 58^\circ$$

The value of $y$ is \boxed{\text{58^\circ}}.