Consecutive Interior Angles in Parallel Lines

Consecutive Interior Angles in Parallel Lines

How to solve consecutive interior angles in parallel lines problems: definition, theorem, example, and its solution.

Definition

By two lines and a transversal, 2 pairs of consecutive interior angles are formed.

By two lines and a transversal,
2 pairs of consecutive interior angles are formed.
(plain blue-purple angles, dotted blue-purple angles)

Theorem

If a transversal passes through parallel lines, then a pair of consecutive interior angles (blue) is supplementary angles.

If a transversal passes through parallel lines,
then a pair of consecutive interior angles is supplementary.

m∠(purple) + m∠(blue) = 180

Example

Find the value of x. The measures of the consecutive interior angles in parallel lines: 5x + 60, 70

These two horizontal lines are parallel.
So the given consecutive interior angles are supplementary.

So (5x + 60) + (70) = 180.