Question

1. which of these statements is correct? determine if there is enough information to show that the lines are parallel to one another. if there is, tell which postulate or theorem you would use. there is enough information. use the converse of the consecutive interior angles theorem. there is enough information. use the converse of the corresponding angles postulate. there is not enough information. there is enough information. use the consecutive interior angles theorem.

Explanation:

Step1: Recall parallel - line theorems

The Converse of the Consecutive Interior Angles Theorem states that if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. The Converse of the Corresponding Angles Postulate states that if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

Step2: Analyze the given angles

We are given two angles: \(50^{\circ}\) and \(130^{\circ}\). These two angles are consecutive - interior angles. Since \(50^{\circ}+130^{\circ}=180^{\circ}\), they are supplementary.

Step3: Apply the relevant theorem

Based on the Converse of the Consecutive Interior Angles Theorem, since the consecutive interior angles are supplementary, we can determine the parallel - ness of the lines.

Answer:

There is enough information. Use the Converse of the Consecutive Interior Angles Theorem.