Question

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. 2. which of these statements is correct? there is not enough information. there is enough information. use the converse of the alternate exterior angles theorem. there is enough information. use the alternate exterior angles theorem. there is enough information. use the converse of the corresponding angles postulate.

Explanation:

Step1: Recall parallel - line postulates and theorems

Parallel lines have several associated postulates and theorems such as the Corresponding Angles Postulate, Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem etc.

Step2: Analyze the given angles

We are given two angles that are equal and they are alternate exterior angles.

Step3: Apply the relevant theorem

The Converse of the Alternate Exterior Angles Theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the two lines are parallel. Since we have two equal alternate exterior angles (both 87°), we can conclude that there is enough information to show that the lines are parallel using the Converse of the Alternate Exterior Angles Theorem.

Answer:

There is enough information. Use the Converse of the Alternate Exterior Angles Theorem.