What Are Supplementary Angles?

By: Mitch Ryan  | 
If you squint, this almost looks like a sunset, but what we actually have here is one angle highlighted in blue and the other angle (the supplementary angle) highlighted in orange. Dream01 / Shutterstock

You've probably seen supplementary angles examples in your everyday life without knowing it. Whether you pass a leaning sign on a flat highway or walk by a shed with a lean-to roof — whenever two angles combine to form a straight, linear pair, there they are.


A Brief Overview of Supplementary and Complementary Angles

Complementary and supplementary angles are two important aspects of geometry that help people navigate and visualize space. However, unless you've dusted off your high school textbooks lately, these concepts are likely fuzzy memories of a bygone era.

Although complementary and supplementary angles both involve combining two different angles, they vary slightly. Two complementary angles add up to 90 degrees (a right angle), while larger combinations called supplementary angles add up to 180 degrees (a straight line).


The difference between complementary and supplementary angles boils down to the sum of two angles needed to create these shapes. Two acute angles can combine to form a right angle (complementary), while two obtuse angles will create a third angle larger than 180 degrees (nonsupplementary).

What Is the Difference Between an Obtuse Angle and an Acute Angle?

The definitions of obtuse and acute are based on their relation to 90-degree right angles. A larger angle that extends past this L-shape is considered obtuse, while a smaller angle creating a V-shape is acute.


Two Angles Are Supplementary When They Make a Straight Angle

Supplementary angles form a straight line. In other words, if you were to use the figure of a circle with a sum of 360 degrees as an example, two supplementary angles add up to 180 degrees to form a measure that splits the circle perfectly in half.


What Are Non-adjacent Supplementary Angles?

Non-adjacent supplementary angles are any two angles that equal 180 degrees when combined. They are called non-adjacent angles because they do not share a common arm or a common vertex (intersecting point).


How Do You Find Supplementary Angles?

Aside from critical practice problems for a midterm, one of the most practical, real-life geometry applications is the ability to find a missing angle. In terms of supplementary angles, this becomes a simple algebra equation.

For example, one angle is 130 degrees. To find the supplementary second angle to the given angle, simply subtract 130 from 180 degrees. If you deduced that the unknown angle is 50 degrees, you are right on target.