Remote Interior Angles: Definition & Examples

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Find the Measure of an Inscribed Angle

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

Replay
Your next lesson will play in 10 seconds
• 0:03 What Is a Remote…
• 1:08 Remote Interior Angle Examples
• 4:14 Lesson Summary
Save Save

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed Speed Audio mode

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Deborah Schell

Deborah teaches college Accounting and has a master's degree in Educational Technology and is holds certifications as a CIA, CISA, CFSA, and CPA, CA.

Triangles contain three inside, or interior, angles that when added together, total 180 degrees. In this lesson, you will learn how to calculate remote interior angles.

What Is a Remote Interior Angle?

Let's meet Rachel, who's learning about geometry in her math class. She has a gymnastics meet next week and will miss the class when she would learn about remote interior angles. She has read the textbook, but she's still confused about how to calculate them. Let's see if we can help Rachel with this problem.

A triangle contains three inside or interior angles that add up to 180 degrees. If we extend any of the sides of a triangle, it will form an outside or exterior angle.

In this example, angles a, b, and c are interior angles, and angles d, e and f are exterior angles.

Remote interior angles are those that don't share a vertex or corner of a triangle with the exterior angle.

In our example, angle d is an exterior angle, and angle a and angle b are the remote interior angles of angle d.

It is easy to calculate the measure of the exterior angle as it is the sum of the two remote interior angles.

In this example, the following is true:

angle d = angle a + angle b

Examples Using Remote Interior Angles

Before we look at some examples, let's review what we know about triangles. As we already stated, the three interior angles of a triangle add up to 180°. You may also recall that when you extend the line of a triangle, you not only create an exterior angle, but you also create a straight line. A straight line also measures 180°, so this means that the sum of the exterior angle and the adjacent angle (the angle next to the exterior angle) equals 180°. Knowing these two facts will make it very easy for you to solve for the unknown angles in the following examples.

Example #1

Let's help Rachel solve for the unknown angle, y, in the following diagram:

First, let's identify the interior and exterior angles. The exterior angle would be 45°, and the interior angles are 30°, 135° and angle y. We can use remote interior angles to solve for the unknown angle y as we know the following is true:

45° = 30° + angle y

Therefore,

angle y = 15°

We can check this answer as we know that the three interior angles in a triangle must add up to 180°. Therefore:

30° + 135° + 15° = 180°

Example #2

Let's help Rachel work through another example where we don't know the exterior angle.

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

Register to view this lesson

Are you a student or a teacher?

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

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.