In the diagram, find the values of x and y.

The angle $x$ and the angle $40^\circ$ are vertically opposite angles. Vertically opposite angles are equal.

$$x = 40^\circ$$

The angle $y$ and the angle $40^\circ$ form a linear pair (angles on a straight line). Angles on a straight line sum to $180^\circ$.

$$y + 40^\circ = 180^\circ$$

Subtract $40^\circ$ from both sides:

$$y = 180^\circ - 40^\circ$$ $$y = 140^\circ$$

The angles are $\boxed{x = 40^\circ}$ and $\boxed{y = 140^\circ}$.