Question

the diagram below shows the map of four straight roads forming 16 numbered angles.
jefferson road
washington road
maple road oak road
which statement is true?
a. angle 10 is congruent to angle 15 is enough information to prove that maple and oak roads are parallel.
b. angle 4 is congruent to angle 16 is enough information to prove that maple and oak roads are parallel.
c. angle 4 is congruent to angle 16 is enough information to prove that jefferson and washington roads are parallel.
d. angle 10 is congruent to angle 15 is enough information to prove that jefferson and washington roads are parallel.

Explanation:

• For option A: ∠10 and ∠15 are not a pair of angles (like alternate interior, corresponding, etc.) that can be used to prove Maple and Oak Roads are parallel, as they are formed by different transversals relative to these roads.
• For option B: ∠4 and ∠16 do not form a valid angle pair to prove Maple and Oak Roads are parallel; their congruence does not relate to the parallelism of these two roads.
• For option C: ∠4 and ∠16 are not a relevant angle pair (e.g., corresponding, alternate interior) for proving Jefferson and Washington Roads are parallel.
• For option D: ∠10 and ∠15 are alternate exterior angles formed by transversal Oak Road intersecting Jefferson and Washington Roads. If alternate exterior angles are congruent, the two lines (Jefferson and Washington Roads) are parallel, which fits the parallel line converse theorem.

Answer:

D. Angle 10 is congruent to angle 15 is enough information to prove that Jefferson and Washington Roads are parallel.