Consecutive Interior Angles: Definition & Theorem

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Exterior Angle Theorem: Definition & Formula

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 What Are Consecutive…
  • 0:44 Identifying…
  • 1:40 The Theorem
  • 2:23 Using the Theorem
  • 3:21 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you will learn what a transversal has to do with consecutive interior angles as well as learning how the theorem ties in with parallel lines. Finally, you will see the information in action.

What Are Consecutive Interior Angles?

When you have two random lines that are cut by a third line, the pairs of angles that are between the two lines and on the same side of the third line are your consecutive interior angles. Look at the following figure which shows the consecutive interior angles.

The two angles circled in blue make one pair of consecutive interior angles, and the other two angles circled in red make another pair of consecutive interior angles. Notice how both pairs are between the two lines and are both on the same side of the third line. We call the third line, or the line crossing the other two lines, the transversal.

Identifying Consecutive Interior Angles

From this definition, you'll see problems asking you to identify angles that are consecutive interior angles. The problem will ask if you can identify which other angle is the consecutive interior angle to a particular angle. You will see a picture like the following and will be asked if you can find the consecutive interior angle to angle 3, for example.

Your job is to look at the picture and choose the other angle that matches up with the angle they gave you. In this example, the angle that pairs with angle 3 is angle 5 because it is on the same side of the transversal and is also between the two lines. If they asked you to find the consecutive interior angle to angle 2, you'd look at the picture and see that angle 2 is outside the two lines. Your answer would be that there is no consecutive interior angle to angle 2 because angle 2 itself is not part of a pair.

The Theorem

Now that we know how to identify consecutive interior angles, let's talk about the theorem. The consecutive interior angles theorem states that when the two lines are parallel, then the consecutive interior angles are supplementary to each other. Supplementary means that the two angles add up to 180 degrees.

supplementary consecutive interior angles

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support