what are remote interior angles

If you’re a fan of geometry, then you’ve probably come across the term “remote interior angle.” But for those who are new to this concept, it may sound like a complex and intimidating idea. Fear not! In this blog post, we’ll break down what remote interior angles are, how they work, and why they matter. So get ready to expand your geometric horizons and discover some fascinating insights into the wonderful world of math!

What is a remote interior angle?

Remote interior angles are a type of angle that play an important role in geometry. An interior angle is formed when two lines intersect, and the remote interior angle is simply the angle formed by one of those lines and a third line that extends from it.

To visualize this, imagine you have three points on a plane: A, B, and C. If you draw lines connecting each pair of points (AB, AC, BC), then you’ll have three angles where those lines meet. The remote interior angle is the one opposite to the side or segment not contained within it.

Measuring remote interior angles can be somewhat tricky because they don’t share any sides with the adjacent angles. However, there is a formula for calculating them if you know the other two angles in your triangle.

Understanding what remote interior angles are and how to measure them is important because they can help us solve all sorts of geometric problems. Whether we’re designing buildings or analyzing complex mathematical models, knowing about these types of angles gives us another tool to work with when tackling challenging tasks!

How to measure a remote interior angle

Measuring a remote interior angle is an essential aspect of geometry. It helps to determine the relationship between angles in polygons. The process of measuring a remote interior angle involves finding the measure of the exterior angle and subtracting it from 180 degrees.

To start, draw a line segment that extends from one vertex of the polygon to another point outside it. Then, extend another side adjacent to this vertex until it intersects with the extended line segment forming an exterior angle.

Next, use your protractor to measure this exterior angle. Remember that an exterior angle is always equal to the sum of its two corresponding interior angles. Therefore, divide this value by two to get one corresponding remote interior angle.

Subtract this result from 180 degrees since all angles in any polygon add up to 180 degrees. Repeat these steps for other vertices if necessary.

By following these simple steps, you can accurately measure any remote interior angle within a polygon effectively and efficiently!

Types of remote interior angles

There are three types of remote interior angles: acute, obtuse, and reflex.

An acute remote interior angle is an angle that measures less than 90 degrees and is formed by two lines intersecting on the same side of a transversal. This means both rays point inside the adjacent angles.

An obtuse remote interior angle is an angle that measures more than 90 degrees but less than 180 degrees and is also formed by two lines intersecting on the same side of a transversal. In this case, one ray points outside while other rays point inside to the adjacent angles.

A reflex remote interior angle is an angle that measures between 180-360 degrees and can be found in concave polygons with at least five sides. In these cases, all rays point towards any internal part of surrounding angles rather pointing inside or outside them.

Each type has its unique characteristics which help us understand different shapes we encounter in our daily lives. By understanding these types we can measure their sizes accurately making it easier for architects & designers to make accurate calculations when planning construction projects or furniture designs.

The importance of remote interior angles

Remote interior angles may seem like a trivial aspect of geometry, but they hold great importance in many real-world applications. One such application is in the design and construction of buildings. Architects and engineers use remote interior angles to determine the exact dimensions of rooms and other spaces within a building.

Another important aspect of remote interior angles is their relationship to exterior angles. By understanding how these two types of angles relate to each other, mathematicians can solve complex problems related to shapes and spatial relationships.

In addition, remote interior angles play an important role in navigation, particularly for pilots who need to calculate flight paths based on the position of stars or other celestial bodies. By understanding how these angles work, pilots can plot accurate courses that take into account factors such as wind speed and direction.

While remote interior angles may not be immediately obvious or intuitive, they are crucial components in many different fields and have numerous practical applications that make them well worth studying.


After delving into the topic of remote interior angles, it’s clear that they play an important role in geometry and mathematics. These angles are formed by two non-adjacent interior angles of a polygon and can be measured using various methods, such as subtracting the sum of adjacent angles from 180 degrees.

There are different types of remote interior angles including consecutive, opposite, and exterior. Each type has its own unique properties and formulas for measurement.

Remote interior angles may seem like a small aspect in geometry but they have significant implications in real-world applications such as architecture, engineering, and construction. Understanding these concepts is crucial for professionals working in these fields to ensure accuracy in their work.

In summary, remote interior angles may not be the most exciting topic but they hold importance in mathematical concepts and practical applications. By mastering this concept we can improve our understanding of geometry and use it to create accurate designs and structures.


You may also like...