Question

name: date: quiz: parallel lines cut by transversal directions: fill in all angles and solve for the given variable when needed.

Explanation:

Step1: Identify vertical - angle relationship

The angle given is 138°. The vertical - angle to the given 138° angle is also 138° because vertical angles are equal.

Step2: Identify corresponding - angle relationship

Since the lines are parallel and we have a transversal, the corresponding angle to the 138° angle (either above or below the other parallel line in the same relative position) is also 138°.

Step3: Identify alternate - interior and alternate - exterior angle relationships

The alternate - interior and alternate - exterior angles to the 138° angle are 138° because for parallel lines cut by a transversal, alternate - interior and alternate - exterior angles are equal.

Step4: Identify supplementary angles

The angles that are supplementary to the 138° angles (adjacent angles that form a straight - line with the 138° angles) are \(180 - 138=42^{\circ}\). And all the other angles that are vertical, corresponding, alternate - interior, or alternate - exterior to these 42° angles are 42°.

Answer:

The angles are either 138° or 42°. There is no variable given to solve for.