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Adjacent Angles

Adjacent angles are the angles that have a common arm (side) and a common vertex, however, they do not overlap. An angle is formed when two rays meet at a common endpoint and adjacent angles are those angles that are always placed next to each other. When the sum of two adjacent angles is 180° then they are called a linear pair of angles. Let us learn more about adjacent angles and see some adjacent angles examples.

What are Adjacent Angles?

Two angles are said to be adjacent angles, if they share a common vertex, a common side, and do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they share a common side BD and a common vertex B.

Adjacent Angles Diagram

Adjacent Angles Definition

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Adjacent Angles Examples

We can see many real-life examples of adjacent angles:

Examples of Adjacent Angles

Properties of Adjacent Angles

The properties of adjacent angles given below help us identify them easily.

Adjacent Supplementary Angles

What is the sum of adjacent angles? The adjacent angles will have the common side and the common vertex. Two angles are said to be supplementary angles if the sum of both the angles is 180 degrees. If the two supplementary angles are adjacent to each other then they are called a linear pair. Sum of two adjacent supplementary angles = 180 degrees.

Linear Pair Example

Adjacent Angles - Linear Pair

A pair of adjacent angles whose measures add up to form a straight angle are called a linear pair. For example, ∠POB and ∠POA are adjacent and supplementary:

Linear Pair Example

The angles ∠POB and ∠POA are formed at O. ∠POB and ∠POA are adjacent angles and they are supplementary i.e. ∠POB + ∠POA = ∠AOB = 180°
∠POB and ∠POA are adjacent to each other and when the sum of adjacent angles is 180° then such angles form a linear pair of angles.


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