Consecutive Interior Angles (Same-Side Interior Angles): Definition, Rule, Examples, and Practice

What are consecutive interior angles?

Consecutive interior angles are two angles inside two lines and on the same side of a transversal.

They are also called same-side interior angles. Some books call them co-interior angles.

The word interior means between the two lines. Consecutive means they are next to each other along the transversal.

Consecutive interior angle rule

Use this rule when the two lines are parallel.

Consecutive interior angles add to 180° when parallel lines are cut by a transversal.

That means they are supplementary angles because their total is 180°.

How to identify the pair

Step 1: Find the transversal, the line that crosses the other two lines.

Step 2: Look between the two crossed lines. That is the interior region.

Step 3: Choose the two interior angles on the same side of the transversal.

If the crossed lines are parallel lines, those two angles add to 180°.

Position chart

This chart separates the key words in the name.

The angles must be interior and on the same side. If one angle is outside the lines, or if the angles switch sides, it is a different relationship.

Consecutive interior vs other angle pairs

Consecutive interior angles are inside the parallel lines and stay on the same side of the transversal.

Z angles, also called alternate interior angles, are inside the lines but switch sides of the transversal.

Corresponding angles sit in matching positions at the two crossings.

Worked example

Problem: Two parallel lines are cut by a transversal. One consecutive interior angle is 124°. What is the other consecutive interior angle?

Step 1: Consecutive interior angles add to 180°.

Step 2: Subtract: 180° - 124° = 56°.

Answer: The other angle is 56°.

Using algebra

If the angles are written as expressions, add the expressions and set the total equal to 180.

Example: the angles are x + 25 and 2x + 5.

Write x + 25 + 2x + 5 = 180. Then 3x + 30 = 180, so x = 50.

Common mistakes

Do not set consecutive interior angles equal. They usually have different measures.

Do not use the 180° rule unless the two lines are parallel.

Do not forget that these angles are supplementary angles only when the parallel-line condition is true.

Quick practice

1. If one consecutive interior angle is 70°, the other is 110° when the lines are parallel.

2. If one angle is 93°, the same-side interior partner is 87°.

3. If the pair is inside but on opposite sides of the transversal, it is not consecutive interior.

4. Consecutive interior angles are also called same-side interior angles.