1. **Problem statement:** We are given four lines with two pairs of parallel lines: $p \parallel t$ and $r \parallel s$. There is an angle labeled $130^\circ$ and another angle labeled $x^\circ$. We need to find the value of $x$. 2. **Key concept:** When two lines are parallel, alternate interior angles are equal. Since $p \parallel t$ and $r \parallel s$, the angle of $130^\circ$ is alternate interior to the angle adjacent to $x$. 3. **Step-by-step solution:** - The angle adjacent to $x$ and $x$ form a linear pair, so their sum is $180^\circ$. - Let the angle adjacent to $x$ be $y$. Since $130^\circ$ is alternate interior to $y$, we have: $$y = 130^\circ$$ - Using the linear pair relationship: $$x + y = 180^\circ$$ Substitute $y = 130^\circ$: $$x + 130^\circ = 180^\circ$$ - Solve for $x$: $$x = 180^\circ - 130^\circ$$ $$x = 50^\circ$$ 4. **Final answer:** $$\boxed{50}$$ Therefore, the value of $x$ is 50 degrees.