Supplementary angles formed by parallel lines and transversals that are both outside the parallel line and on the opposite side of the transversal line

Answer: Supplementary angles are two angles whose measures add up to 180 degrees. When you have a pair of parallel lines that are cut by a transversal, several pairs of these angles are formed. Specifically, we're interested in the angles that are outside the parallel lines and on opposite sides of the transversal.

To identify supplementary angles in this situation, look for angles that are known as consecutive exterior angles. Consecutive exterior angles are formed on the outside of two parallel lines on opposite sides of the transversal, and they are supplementary. Therefore, each pair of consecutive exterior angles will add up to 180 degrees.

Here are the steps to identify supplementary angles formed by parallel lines and a transversal that are outside the parallel lines and on opposite sides of the transversal:

1. Identify the two parallel lines and the transversal that cuts across them. 2. Locate the angles that are outside the parallel lines, which means they are not between the two lines. 3. From these outside angles, find the ones that are on opposite sides of the transversal. These are your consecutive exterior angles. 4. Verify that these angles are supplementary by either measuring them with a protractor or by using other known angle relationships to calculate their measures.

For example, if one consecutive exterior angle is given as 120 degrees, the angle supplementary to it must be 180 - 120 = 60 degrees because the sum of supplementary angles is always 180 degrees.