Adjacent angles are two angles which share a common side while also having a common vertex without overlapping.

If there is a lack of one of these properties, it is simply not an adjacent angle. In simple terms, they are two angles that are beside each other. Let’s break down the common terms we use when talking about them.

Other Important Definitions

Before getting into the details, here are other important definitions you should keep in mind:

•Common vertex: a point of intersection that is shared by two or more rays or lines.

•Common side is one line, ray, or line segment used to create two angles sharing the same vertex. Both angles use the common side and one other side.

•Ray is a line that has a fixed starting point but an undefined end point.

•Line Segment is a line that has two endpoints.

What are the properties of adjacent angles?

Now that we’ve defined the basic idea of what they are, let’s discuss how to identify them. Here are the six fundamental properties you need to know:

•They share a common side and vertex.

•They never overlap.

•There’s always a non-common arm on both sides of the common arm.

•They can be complementary (measures adding up to 90˚) or supplementary (measures adding up to 180˚) if they share a common angle.

How To Identify Adjacent Angles

There are two properties that can help you identify them easily: If they share a common side (arm) and vertex. If only one of these properties is satisfied in two angles, then they are not adjacent angles.

Examples

In the real world you can see many examples of adjacent angles like:

• Two connected pieces of pizzas with the middle divider being the shared side.
• The hour, minute, and second hands on a clock.

Linear Pairs

In geometry, one of the most common examples is a linear pair in which two angle measures add up to form a straight angle (180˙). Here’s an example:

Frequently Asked Questions

Are adjacent angles congruent?

They can sometimes be congruent. “Congruent” means exactly equal as far as shape and “adjacent” means “next to”. So when two angles have the exact same angle measurement they are equal. But, if they don’t, they would not be considered congruent.

Are adjacent angles complementary?

Adjacent and non-adjacent angles can be complementary if they add up to 90 degrees. Two angles are said to be complementary if they add up to 90 degrees. 

Are adjacent angles equal to 180?

Adjacent angles can equal to 180˙, but not in all cases. As mentioned above, supplementary adjacent angles add up to 180˙but if the adjacent angles are not linear pairs, then they won’t add up to 180˙.

Solutions For Common Problems

•Draw and label two adjacent angles for which the sum of their measures is 90˙
•Use the terms adjacent angles, linear pair, or neither to describe angles 1 and 2 in as many ways as possible.
•How many pairs of adjacent angles are in the design of the window shown at the right? Name them.
•Draw a pair of adjacent angles that are complementary and have the same measure. What is the measure of each angle?
•If the measure of one angle of a parallelogram increases, what happens to the measure of its adjacent angles so that the figure remains a parallelogram?

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