1. The problem states that ABC and FBD are straight lines with $x + y = 142^\circ$. We need to find $x$, $y$, and $z$. \n\n2. Since ABC is a straight line, the angles on it must sum to $180^\circ$. Similarly, the straight line FBD also has angles summing to $180^\circ$.\n\n3. Given $x + y = 142^\circ$, and knowing straight line ABC makes $180^\circ$, the remaining angle adjacent to $x + y$ on line ABC is $180^\circ - 142^\circ = 38^\circ$.\n\n4. The angle $z$ is vertically opposite to this $38^\circ$ angle at point B because z is the angle between BF and BD, and the $38^\circ$ angle is the supplementary angle on the straight line ABC. Vertically opposite angles are equal.\n\n5. Therefore, $z = 38^\circ$.\n\n6. To find values for $x$ and $y$, unless additional information is given about the relation between $x$ and $y$, or any specific angle values, they cannot be uniquely determined apart from the fact that $x + y = 142^\circ$. \n\nFinal answers:\n\nx + y = 142^\circ\n\nz = 38^\circ