Question

Determining Which Lines Are Parallel
Carmen is designing an intersection of the rail line and four streets. She wants to know which streets are parallel.

Transversal t crosses lines c, d, e, f forming 16 angles. Clockwise from top left, the angles formed with line c are blank, blank, blank, 114 degrees; with line d are blank, blank, 68 degrees, blank; with line e are blank, 112 degrees, blank, blank; with line f are blank, blank, 66 degrees, blank.

Which streets are parallel? Check all that apply.
c || d
c || e
c || f
d || e
d || f
e || f

Answer 1

Answers: c || f and d || e.

Reason: Use vertical and linear-pair angles to fill in the missing measures.
- At c: bottom-left = 114 → top-right = 114 (vertical), so top-left and bottom-right = 66 (supplementary).
- At d: bottom-right = 68 → top-left = 68, so top-right and bottom-left = 112.
- At e: top-right = 112 → bottom-left = 112, so top-left and bottom-right = 68.
- At f: bottom-right = 66 → top-left = 66, so top-right and bottom-left = 114.

Thus c and f have identical angle positions (66,114,66,114) so c || f; d and e match (68,112,68,112) so d || e. All other pairs are not parallel.