Question

Lines p and q are cut by a transversal. At the intersection of line p with the transversal, the bottom right angle is x. At the intersection of line q with the transversal, the bottom left angle is y and the bottom right angle is z.
Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? Check all that apply.

x = z
x + y = 180°
x + z = 180°
x = y
z = 180°

Answer 1

Answer: x = z only.

Reason: x and z are corresponding angles (same relative position at the two intersections). If corresponding angles are equal, the lines are parallel. The other equations do not correspond to the standard parallel-line criteria:

- x + y = 180°: x and y are not a same-side interior (consecutive interior) pair, so their supplementarity does not force the lines to be parallel.
- x + z = 180°: that could occur for some nonparallel configuration (it would force x = z = 90° if the lines were parallel, but equality to 180° by itself doesn't imply parallelism).
- x = y: these are not corresponding or alternate interior angles, so equality doesn't guarantee parallelism.
- z = 180°: impossible for a proper angle at an intersection (and does not imply the two lines are parallel).