Final answer:
The question involves proving that two angles are supplementary based on given parallel line conditions. By using the definitions of parallel lines and supplementary angles, we can conclude that if two sets of parallel lines are intersected by a transversal, the angles forming a straight line will be supplementary, summing to 180 degrees.
Step-by-step explanation:
To resolve the student's question, we need to prove that angles 1 and 2 are supplementary when a // b and c // d. Supplementary angles are two angles whose sum is 180 degrees. Since the lines a and b are parallel, as well as lines c and d being parallel, any angles that form a straight line when these sets of lines intersect will indeed be supplementary.
Option 1 suggests proving that angles 1 and 2 form a straight line, which, due to the Parallel Postulate, would inherently mean they are supplementary. When a pair of parallel lines is intersected by a transversal, the corresponding angles are equal. If another set of parallel lines intersects the transversal in the same set of corresponding angles, the angles created (1 and 2) will lie on a straight line.
Option 2 suggests proving that the sum of angles 1 and 2 is 180 degrees, which is a direct consequence of Option 1 and falls under the definition of supplementary angles. Option 3 and Option 4 are incorrect, as being parallel does not imply that angles are equal or complementary (sum of angles being 90 degrees).
The correct proof would involve demonstrating Option 1 or Option 2, that the angles are supplementary, and this follows from the fact that a straight line measures 180 degrees, so any two adjacent angles that form a straight line are supplementary.