Question

given m∠3 + m∠8 = 180°. which lines are parallel, if any must be parallel, based on the given information? c || d by the converse of the same - side interior angles theorem. a || b by the converse of the corresponding angles theorem. c || d by the converse of the alternate interior angles theorem. not enough information to make a conclusion.

Explanation:

Step1: Recall angle - relationship theorems

Same - side interior angles are supplementary (add up to 180°) when two lines are parallel. Alternate interior angles are equal when two lines are parallel. Corresponding angles are equal when two lines are parallel.

Step2: Identify the position of ∠3 and ∠8

∠3 and ∠8 are same - side interior angles formed by lines c and d with a transversal.

Step3: Apply the theorem

Since m∠3 + m∠8=180°, by the converse of the same - side interior angles theorem, lines c and d are parallel.

Answer:

c || d by the converse of the same - side interior angles theorem