Answer:
Please read the assumptions that lead to the proposed answer of options a, b, and e being correct. Options c and d are easily rejected. The question is ambiguous about the locations of the angles.
Explanation:
Parallel lines have slopes that are identical. Lines p and q have the same slopes.
It is difficult imagining what angles are represented by x, y, and z. There are only 2 lines, and they do not intersect. The locations of the angles are not identified. The lack of an intersecting point means it is free range as to where we assign the angles.
The attached graph illustrates some possibilities for x, y, and z. It uses two simple equations as examples, with the same slope to make them parallel. Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines. Even then, there aren't many unique locations for the angles. To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.
Even with this huge step, there is limited information to be able to identify which of the answer options is correct. We can say that:
x = z
x+y=180
y+z=180
The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid. Looking at the answer options, we can match choices a, b, and e to the conclusions above. d makes no sense because it is not an equation. c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel. The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.
Answer Options Guarantee Parallel?
a. x = z Yes
b. x + y = 180 degree Yes
c. x + z = 180 degree No
d. x + y No
e. y + z = 180 Yes