Final answer:
If two lines in a plane are cut by a transversal, and on the same side of the transversal there are two acute angles or two obtuse angles, these angles are supplementary, meaning they add up to 180°.
Step-by-step explanation:
If two lines in a plane are cut by a transversal, then any two angles that are on the same side of the transversal and are both acute angles or both obtuse angles are supplementary. This means the sum of the two angles is 180°.
When two lines are intersected by a transversal, eight angles are formed. Angles that are on the same side of the transversal and inside the two lines are called consecutive interior angles if both lines are parallel, and they add up to 180°, making them supplementary. If the angles are outside the two lines but on the same side of the transversal, they are called consecutive exterior angles, and these would also be supplementary if the lines are parallel.
However, if the two intersected lines are not parallel, then there is no guarantee that the consecutive interior or exterior angles will be supplementary; they all depend on the specific angles of the lines.