Consecutive interior angles are angles formed between a transversal line and two parallel lines. Knowing how to identify pairs of consecutive interior angles will help you in solving for unknown angles found within parallel lines.

## What Are Consecutive Interior Angles?

Consecutive interior angles are angles formed when a transversal line cuts through two parallel lines. **These are interior angles formed within the inner region of the two parallel lines. At the same, they lie non-adjacent to each other and are found on the same side.** Use this quick guide when identifying consecutive interior angles:

- The pair of interior angles that lie within the parallel lines.
- They must not share the same vertex.
- They, however, lie on the same side of the parallel lines’ inner region.

Take a look at the two parallel lines, *m* and *n*, cut through by a transversal line shown above. You can always find four interior angles inside the parallel lines’ region such as the following: ∠3, ∠4, ∠5, and ∠6. Consecutive interior angles lie on the same side, so we have the following **pairs of consecutive interior angles: ∠3 & ∠5 and ∠4 & ∠6**.

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After learning how to identify consecutive interior angles, it’s time to test your knowledge by applying what you’ve learned so far!

#### Example 1

A transversal line passes through the pair of parallel lines, *s* and *t*. Eight angles are formed as shown above. Which of the following pair of angles are consecutive interior angles?

A. *∠a* and *∠e*

B. *∠a* and *∠g*

C. *∠d* and *∠f*

D. *∠c* and *∠f*

First, identify the four interior angles that you can find from the parallel lines. These are the angles found within their inner region. Hence, we have the following angles: *∠c*, *∠d*, ∠*e*, and *∠f*. This means that *∠a* & *∠e* and *∠a* & *∠g* couldn’t possibly be pairs of consecutive interior angles eliminating A and B.

While the pair of angles, *∠c* and *∠f*, are interior angles, they are not found on the same side. Now, taking a look at C: *∠d* and *∠f* are interior angles lying on the same side confirming that the two are consecutive interior angles. This shows that **C is the correct answer**.

## Consecutive Interior Angle Theorem

The consecutive interior angle theorem states that **any pair of consecutive interior angles are supplementary** (or add up to 180°).

This means that given the consecutive interior angles, ∠3 & ∠5 and ∠4 & ∠6, each pair will add up to 180°.

∠3 + ∠5 = 180°

∠4 + ∠6 = 180°

Keep this property in mind when solving problems involving parallel lines and their angles. Remember that any pair of consecutive interior angles will always be supplementary.

#### Example 2

If ∠c has an angle measure of 70°, what is the measure of ∠e?

The angles, ∠c and ∠e, are consecutive interior angles, so they are supplementary. This means that the sum of their angle measures is equal to 180°.

Hence, **∠e has an angle measure of 110°**.