Adjacent angles are an important concept to understand in maths. They are a key concept in geometry and are usually introduced in 4th grade maths.
Although kids study angles in their math courses throughout their time at school, it’s often a difficult concept to grasp. If your child is struggling with understanding not only angles, but any other concepts in maths, you may want to consider tutoring courses.
In order to help you or your child on your journey to understanding angles, we have put together this little guide to walk you through the key concepts, definitions and FAQs surrounding adjacent angles.
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Adjacent Angles Definition
Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way. When you break down the phrase adjacent angles, it becomes easy to visualise exactly what it is; they are two angles that are next to each other.
How do you identify adjacent angles?
Being able to identify a common side and a common vertex is the simplest way to identify an adjacent angle. If two angles share one side and both derive from the same corner (vertex) point, then they are adjacent angles.
It’s important to remember that adjacent angles must have BOTH a common side and common vertex. Therefore, if you see two angles that are coming from the same corner but there is another angle in the middle, it means that they do not share any sides. This means that they are not adjacent angles as they don’t share a side AND a vertex.
Identifying adjacent angles becomes easier with practice and seeing examples will help you understand what you are looking for.
What is the difference between vertical and adjacent angles?
Identifying the difference between adjacent angles and vertical angles is an important skill to master in geometry. The best way to visualize the difference between these two types of angles is to imagine two straight lines intersecting each other to form a cross.
When a cross is formed, four angles are formed. We know how to identify the adjacent angles, because they have a common side and a common vertex. But how do we identify a vertical angle? Identifying a vertical angle is equally as easy as finding an adjacent angle. Similarly to adjacent angles, a set of vertical angles will share a vertex point. However, they do not need to share a common side.
When thinking about a cross, the vertical angles are the angles that are opposite each other. This is why they are sometimes called vertically opposite angles.
What are the properties of adjacent angles?
In order to further help you visualize what adjacent angles look like, here’s a quick list of their properties:
- They share a common side
- They share a common vertex
- The angles do not overlap
- Although they share a common side (common arm) in the centre, the other side is not shared (non-common arm)
- They do not have a common interior point
- They can be complementary angles or supplementary angles
What are adjacent angles examples?
Linear Pair
In order to understand what a linear pair looks like, you must imagine a cross. When two lines intersect, four angles are created. 
If you take a look at the picture to the right, you can see that there are four angles labelled 1, 2, 3, and 4. In this image, the linear angles are 1 and 3, 3 and 2, 2 and 4, 4 and 1.
You can triple check that two angles are a linear pair by seeing if they add up to 180 degrees. All linear pairs of angles are supplementary and therefore always add up to 180 degrees. If the angles are adjacent and add up to 180 degrees you can be confident in making the assertion that they are a linear pair of adjacent angles.
Vertically Opposite Angles
Vertically opposite angles are technically not adjacent angles, but where you find adjacent angles, you will likely also find some vertically opposite angles.
Vertical angles have already been explored, but to clarify, vertical angles share the same vertex but do not share any of the same sides. If we take the above picture, 3 and 4 and 1 and 2 are considered vertically opposite angles.
A key property of vertically opposite angles is that they measure exactly the same. For example, if angle 1 was 30 degrees, angle 2 would also measure as 30 degrees.
FAQ
1. What are Adjacent Angles?
Put simply, adjacent angles are angles that share a common side and a common vertex (corner point).
2. Are adjacent angles equal to 180?
This is TRUE in some cases! Supplementary adjacent angles always add up to 180. This is because the two angles sit next to each other on a straight line and all angles on a straight line add up to 180.
However, if the adjacent angles are not linear pairs and another angle is in the mix, the two adjacent angles will not add up to 180.
3. Can Vertical Angles be Adjacent?
As vertical and adjacent angles can often exist in a small area together, many people believe that vertical angles can also be adjacent angles. This is FALSE. Vertical angles do not share any of the same sides, meaning they cannot be adjacent.
4. Can adjacent angles be linear pairs?
YES! Adjacent angles can be linear pairs. As linear pairs share both a common side and a common vertex, they can be considered adjacent angles. However, not all adjacent angles are linear pairs.
5. Are adjacent angles 90 or 180 degrees?
As stated previously, pairs of angles can be equal to 180, if the angles are located next to each other on a straight line and the sum of these two angles is equal to 180. The same applies if the two angle measures are equal to 90 (form a straight angle).
For example, they can be made up of an acute angle and a smaller or larger angle. As a reminder, an acute angle measures less than 90 degrees.
6. What is an example of adjacent angles?
In everyday life, the steering wheel is a good example of adjacent angles. If you take a clock (in normal clock form), the hands of the clock form a pair of adjacent angles.
7. How can you tell if angles are adjacent angles?
For example, in this image, angle ABC is adjacent to angle CBD, but angle EFG and angle HIJ are not adjacent angles, since they do not share a common side or vertex. The same applies to angle KLM and LMN: although they share the same side, they don’t share the same vertex. They are therefore nonadjacent angles.
This was a quick run through of adjacent angles to help you get to grips with this integral part of the geometry syllabus. However, there are always more that you can do to ensure you achieve the grade you want.
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