Question

there are some special relationships between angles when the lines cut by the transversal are parallel. complete each statement about the non - adjacent exterior angles. the angles on the same side of the transversal are? . the angles on opposite sides of the transversal are? . options for the second blank: congruent, supplementary. there is a diagram showing two parallel lines cut by a transversal, with angle measures 130° and 50° marked.

Explanation:

Step1: Analyze same - side angles

When two parallel lines are cut by a transversal, same - side exterior angles (non - adjacent) are supplementary. Supplementary angles are angles whose sum is \(180^{\circ}\). Looking at the diagram, for the same - side angles, we have \(130^{\circ}\) and \(50^{\circ}\) on the same side of the transversal, and \(130 + 50=180^{\circ}\), so they are supplementary.

Step2: Analyze opposite - side angles

For angles on opposite sides of the transversal (non - adjacent exterior angles), when the lines are parallel, these angles are congruent. Congruent angles have the same measure. From the diagram, the \(50^{\circ}\) angles on opposite sides of the transversal are equal, and the \(130^{\circ}\) angles on opposite sides of the transversal are also equal. So opposite - side non - adjacent exterior angles are congruent.

Answer:

The angles on the same side of the transversal are supplementary.
The angles on opposite sides of the transversal are congruent.