Let's go through each part of the problem, based on the given figure and the questions:

1. The relation between $x$ and $y$:

   • In the figure, the road and railroad tracks form parallel lines, and $x$ and $y$ are angles formed by a transversal line (the road). Since $x$ and $y$ are on opposite sides of the transversal, but inside the parallel lines, they are alternate interior angles.
   • Answer: A. Alternate interior angle

2. The angle between the angle bisectors of $p$ and $x$:

   • The bisector of an angle divides the angle into two equal parts. If the bisectors of $p$ and $x$ form an angle, it would be half the sum of the angles $p$ and $x$. Since $p$ and $x$ are supplementary angles (they add up to 180°), their bisectors will form an angle of $90^\circ$.
   • Answer: D. 90°

3. Find the values of $y$ and $p$:

   • From the given figure, we know that $y = x$ since they are alternate interior angles. The angle $m$ is given as $50^\circ$. Therefore:
     • $x + 50^\circ = 90^\circ$ (since $x$ and 50° are complementary angles).
     • $x = 40^\circ$.
     • Since $x$ and $y$ are equal, $y = 40^\circ$.
   • $p$ is supplementary to $x$, so $p + x = 180^\circ$. Thus, $p = 180^\circ - 40^\circ = 140^\circ$.
   • Values: $y = 40^\circ$, $p = 140^\circ$.

4. Find the values of $x$ and $m$:

   • We already found that $x = 40^\circ$ and $m = 50^\circ$.
   • Values: $x = 40^\circ$, $m = 50^\circ$.

Let me know if you need further clarification or details. Here are five related questions to deepen your understanding:

1. What is the sum of the interior angles on the same side of a transversal cutting parallel lines?
2. Can you explain why alternate interior angles are equal in parallel lines?
3. What is the relationship between corresponding angles when a transversal cuts two parallel lines?
4. How do angle bisectors behave when the angles are supplementary?
5. What would happen to the values of $p$ and $y$ if the given angle was different?

Tip: Always remember that when dealing with parallel lines and a transversal, alternate interior angles are equal, and co-interior angles sum up to 180°.