Determine the values (s) of the unknown angles.

The lines J and P are parallel, as indicated by the arrows. The line RS is a transversal. Angle $x$ and the $60^\circ$ angle are alternate interior angles. When two parallel lines are intersected by a transversal, alternate interior angles are equal.

$$x = 60^\circ$$

Angles $x$ and $y$ are vertically opposite angles formed by the intersection of line J and line RS. Vertically opposite angles are equal.

$$y = x$$

Substitute the value of $x$ found in Step 1 into the equation from Step 2.

$$y = 60^\circ$$

The values of the unknown angles are:

$$x = \boxed{60^\circ}$$ $$y = \boxed{60^\circ}$$