Final answer:
If two coplanar lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel. This is based on the consecutive interior angles converse theorem.
Step-by-step explanation:
If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary (sum of the angles is 180°), then the two lines are parallel. This relationship between angles and lines is a part of geometrical postulates and theorems that are used to determine various properties of lines and angles in a plane. When the interior angles on the same side of the transversal sum up to 180°, it is a result of the consecutive interior angles converse theorem, which is a commonly used geometric property to ascertain if two lines are parallel.