Question

image by e2020
in the diagram, the lines dividing the parking spaces are parallel. what must be true about \\( \angle 1 \\) and \\( \angle 2 \\)? what theorem supports your conclusion?
a. \\( \angle 1 \\) and \\( \angle 2 \\) are supplementary; alternate interior angles theorem
b. \\( \angle 1 \cong \angle 2 \\); alternate interior angles theorem
c. \\( \angle 1 \\) and \\( \angle 2 \\) are supplementary; consecutive interior angles theorem
d. \\( \angle 1 \cong \angle 2 \\); consecutive interior angles theorem

Explanation:

Step1: Recall the properties of angles formed by parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Alternate interior angles are congruent.

Step2: Analyze the position of ∠1 and ∠2

∠1 and ∠2 are consecutive interior angles.

Step3: Apply the relevant theorem

According to the consecutive interior angles theorem, if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

Answer:

C. ∠1 and ∠2 are supplementary; consecutive interior angles theorem