Question

there are some special relationships between angles when the lines cut by the transversal are parallel. complete each statement about the non - adjacent interior angles. the angles on the same side of the transversal are? the angles on opposite sides of the transversal are? congruent supplementary

Explanation:

Step1: Recall the properties of angles formed by a transversal with parallel lines

When two parallel lines are cut by a transversal, the same - side interior angles have a sum of \(180^{\circ}\). The angles on opposite sides of the transversal (alternate interior angles) are equal in measure.

Step2: Analyze the first blank

For the angles on the same side of the transversal:
Let's take two angles on the same side of the transversal. If we consider \(50^{\circ}\) and \(130^{\circ}\) (or other pairs of same - side interior angles), \(50 + 130=180\). So, the angles on the same side of the transversal are supplementary.

Step3: Analyze the second blank

For the angles on opposite sides of the transversal:
Take the pairs of non - adjacent interior angles on opposite sides of the transversal. For example, the two \(130^{\circ}\) angles (or the two \(50^{\circ}\) angles). They have the same measure. So, the angles on opposite sides of the transversal are congruent.

Answer:

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