What is the sum of co-interior angles in parallel lines?

The sum of co-interior angles in parallel lines is always 180 degrees.

When two parallel lines are intersected by a transversal (a line that crosses both parallel lines), several pairs of angles are formed. Among these pairs are the co-interior angles, also known as consecutive interior angles or allied angles. Co-interior angles are located on the same side of the transversal and inside the parallel lines.

To understand why their sum is 180 degrees, consider the properties of parallel lines and the angles formed. Parallel lines never meet and are always the same distance apart. When a transversal cuts through them, it creates angles that have specific relationships. For co-interior angles, if you add them together, their measures will always total 180 degrees. This is because they are supplementary angles, meaning their measures add up to form a straight line.

For example, if one co-interior angle measures 110 degrees, the other co-interior angle on the same side of the transversal will measure 70 degrees, since 110 + 70 = 180 degrees. This relationship holds true for any pair of co-interior angles formed by a transversal intersecting parallel lines.

Understanding this concept is crucial for solving various problems in geometry, such as finding unknown angle measures or proving that lines are parallel. Remembering that co-interior angles sum to 180 degrees can help you quickly identify and work with these angles in different geometric contexts.