Remote Interior Angles: Definition & Examples

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  • 0:03 What Is a Remote…
  • 1:08 Remote Interior Angle Examples
  • 4:14 Lesson Summary
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Lesson Transcript
Instructor: Deborah Schell

Deborah teaches college Accounting and has a master's degree in Educational Technology.

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.

remote interior 1

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.

remote interior 2

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.

remote interior 3

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:

remote interior 4

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.

remote interior 5

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