What are the adjacent angles, definition, examples, properties || Mathscolor

 In the simplest language, the adjacent angles are " the angles that have a common side (arm) and vertex."  We will see the minute details of adjacent angles which will cover meaning/definition, real life and, relevant examples, how to identify & properties of the angles, and many more.

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What are Adjacent Angles?

As mentioned above the adjacent angles shares a common vertex and side. Such angles can be complementary angles or supplementary angles. Let's understand these angles as well:

  • Adjacent complementary angle:- If the sum of adjacent angles is equal to 90 degrees then angles will be complementary to each other.
  • Adjacent Supplementary angle:- If the sum of adjacent angles is equal to 180 degrees then angles will be supplementary to each other.

Adjacent Angles Definition

" Angles that are next to each other as such that they will share a common vertex and a common side and that too without overlapping each other."

Adjacent Angles Examples

We can relate real-life examples with the adjacent angle, see the below image for the most common example and you will understand in a clear and simple way.

  • Clock:- we can see the hour, minute, and second hand, it is forming adjacent angles and here second hand is the common arm.
  • Pizza:- we can see the slices are placed next to each other and the image clearly shows the real-life example of the adjacent angles.

Properties of Adjacent Angles

Now let's see the properties of the adjacent angles that will help someone to identify them without fail. 

By observing the above image, we can clearly say: 

  • Common Arm - it will always have the common arm.
  • Common vertex - it will share a common vertex.
  • Non-Common Arms (sides) - it will have non-common arms on either side of the common arm.
  • Supplementary or Complementary Angles - It can be either of them according to the angle measurements.
  • Non-common interior point - it will not share any interior point as a common one.

Important Note:

Below are a few points that should be known to you:

  • An acute angle be adjacent to an obtuse angle
  • The two obtuse angles can be adjacent angles
  • If the sum of two adjacent angles is 180, they will be called a linear pair of angles.
  • Linear pair angles are supplementary but all supplementary angles are not linear pair angles.

How to Identify Adjacent Angles?

Simply remember that adjacent angles will be formed when

 " they will share a common side and a common vertex".

If two angles satisfy the above statement then only they can be considered adjacent angles. In case, only sides are common or vertex then avoids considering them as the adjacent angles.

Let's understand it with the below examples

Look at the above image and we can clearly see:

  • Fig 1 is not adjacent - because angle 1 and 2 overlaps with each other.
  • Fig 2 is not adjacent - because they have a common side but not a common vertex.
  • Fig 3 is an adjacent one - It fulls filling the statement " common side and common vertex".


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