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°, they are called a linear pair of angles. Let us learn more about adjacent angles and see some adjacent angles examples.

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 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.

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

• The most common real-life example of adjacent angles can be seen in two pizza slices that are placed next to each other.
• Another common example can be seen in the clock which shows the hour, minute, and second hand forming adjacent angles when all three are away from each other.
• We can find three adjacent angles in the steering wheel of a car.

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

• Adjacent angles always share a common arm.
• They share a common vertex.
• They do not overlap.
• They have a non-common arm on both sides of the common arm.
• Two adjacent angles can be supplementary or complementary based on the sum of the measures of the individual 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.

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:

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.