What are consecutive interior angles?

How to locate the pair

The important theorem is that consecutive interior angles are supplementary when the two crossed lines are parallel. That makes them useful in algebraic angle work and in proofs involving straight-line reasoning spread across two intersections.

The name itself comes from position, not from the number one hundred eighty. Students who separate the layout from the theorem usually read these pairs more accurately.

When the lines are parallel, the two angles are supplementary, so their measures add to 180 degrees. They do not have to look alike. One may be acute while the other is obtuse, but the total still makes a straight-turn amount.

Find the strip between the two lines first. Then choose the two angles on one side of the transversal. If you accidentally choose opposite sides, you have changed the angle relationship and may use the wrong theorem.

• Consecutive interior angles lie on the same side of the transversal between the lines.
• Interior means the pair is between the two lines.
• Consecutive means the two angles are on the same side of the transversal.
• If the lines are parallel, consecutive interior angles add to one hundred eighty degrees.

Where consecutive interior angles help

• Use consecutive interior angles in parallel-line proofs and equation-based angle problems.
• Use them when testing whether two lines are parallel from a supplementary same-side interior pair.
• Use them to explain how one transversal creates inside pairs that add to a straight-angle total.

Three consecutive-interior checks

• Do not choose opposite-side interior angles and call them consecutive interior; that pair is alternate interior instead.
• Do not force a one-hundred-eighty-degree equation unless the parallel condition is given or established.
• Do not confuse the word consecutive with meaning 'nearby' only; the side of the transversal matters precisely.