Question: In the figure below, $h \parallel l$ and $j \parallel k$. Find the values of $z$ and $x$.\n\nThe graph shows two horizontal parallel lines labeled $h$ (top) and $l$ (bottom), and two slanted parallel lines labeled $j$ and $k$; at the top intersection with $j$, the angle below $h$ and to the right of $j$ is $z^\circ$, the angle above $l$ and to the right of $j$ is $70^\circ$, and at the top intersection with $k$, the angle above $h$ and to the left of $k$ is $(4x + 30)^\circ$.\n\n$z = $\n$x = $
1. **State the problem:** We are given two pairs of parallel lines: $h \parallel l$ and $j \parallel k$. We need to find the values of angles $z$ and $x$ based on the given angle measures and parallel line properties.\n\n2. **Identify the relationships:** Since $h \parallel l$ and $j \parallel k$, corresponding and alternate interior angles formed by transversals are equal.\n\n3. **Analyze the angles at line $j$:** The angle below $h$ and to the right of $j$ is $z^\circ$. The angle above $l$ and to the right of $j$ is $70^\circ$. Since $h \parallel l$ and $j$ is a transversal, these two angles are alternate interior angles and therefore equal.\n\n$$z = 70$$\n\n4. **Analyze the angles at line $k$:** The angle above $h$ and to the left of $k$ is $(4x + 30)^\circ$. Since $j \parallel k$, the angle corresponding to $z$ at $j$ is equal to the angle at $k$ on the same side. The angle corresponding to $z$ at $k$ is $z^\circ = 70^\circ$.\n\n5. **Set up the equation for $x$:** The angle $(4x + 30)^\circ$ and the angle $z = 70^\circ$ are supplementary because they form a linear pair on line $h$. So,\n\n$$ (4x + 30) + 70 = 180 $$\n\n6. **Solve for $x$: **\n\n$$ 4x + 30 + 70 = 180 $$\n$$ 4x + 100 = 180 $$\n$$ 4x = 180 - 100 $$\n$$ 4x = 80 $$\n$$ x = \frac{80}{4} $$\n$$ x = 20 $$\n\n7. **Final answers:**\n\n$$ z = 70 $$\n$$ x = 20 $$