Question

question 11 (5 points) listen when ______ angles made by two lines and a transversal are supplementary, the lines are parallel. a) corresponding b) alternate exterior c) same side interior d) alternate interior

Explanation:

To determine the correct answer, we analyze the properties of angles formed by a transversal with two lines:

• Option A (corresponding angles): Corresponding angles are equal when lines are parallel, not supplementary. So A is incorrect.
• Option B (alternate exterior angles): Alternate exterior angles are equal when lines are parallel, not supplementary. So B is incorrect.
• Option C (same - side interior angles): By the converse of the same - side interior angles theorem, if same - side interior angles are supplementary (their sum is \(180^{\circ}\)), then the two lines cut by the transversal are parallel. This matches the given statement.
• Option D (alternate interior angles): Alternate interior angles are equal when lines are parallel, not supplementary. So D is incorrect.

Answer:

C) same side interior