Adjacent Angles
Adjacent angles are the angles with a common arm(side) and a common vertex. An angle is formed by two rays meeting at a common endpoint. For example, two pizza slices next to each other in the pizza box form a pair of adjacent angles when we trace their sides.
1.  What are Adjacent Angles? 
2.  Properties of Adjacent Angles 
3.  Adjacent Angles Examples 
4.  FAQs on Adjacent Angles 
What are Adjacent Angles?
Two angles are said to be adjacent angles, if, they don't overlap they share a common vertex, they share a common side or ray and the other sides of the two angles should lie on opposite sides of the common side.
Look at the below images to get a clear view of adjacent angles. Angle 1 and 2 are adjacent because they have common side BD and common vertex B.
Properties of Adjacent Angles
The following properties listed below help us identify adjacent angles easily.
 They share a common arm.
 They share a common vertex.
 They don't overlap.
 They don't have a common interior point.
 They have a noncommon 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.
Important Notes
Following are the important notes related to the adjacent angles.
 When two angles are adjacent, then their sum is the angle formed by two noncommon arms and one common arm.
 If a ray stands on a straight line, then the sum of adjacent angles formed is 180°.
 If the sum of two adjacent angles is 180° then they are called a linear pair of angles. All linear pairs are supplementary because supplementary angles sum up to 180°. However, all supplementary angles need not be linear pairs. To form a linear pair the lines need to intersect each other and must form adjacent angles.
 If the sum of two adjacent angles is 180° then the noncommon arms form a line.
☛Related Articles on Adjacent Angles
Check out these interesting articles to know more about Adjacent Angles and their related topics.
Adjacent Angles Examples

Example 1: List 5 pairs of adjacent angles in the following figure.
Solution: Five pairs of adjacent angles are given below.
∠AOE, ∠EOC
∠EOC, ∠COB
∠COB, ∠BOD
∠BOD, ∠AOD
∠AOD, ∠AOE

Example 2: Are the angles marked as 1 and 2 in the following figures adjacent? Give reasons for your answers.
Solution: Clearly ∠ 1, ∠ 2 have a common vertex O and a common ray OB. ∠ 1 and ∠ 2 are touching the sides OA, OB(Common side), OC. OA and OC are the opposite sides of the common side OB.
FAQs on Adjacent Angles
What Are Adjacent Angles in Geometry?
Two angles are said to be adjacent angles, if, they have the following characteristics:
 They don't overlap.
 They share a common vertex.
 They share a common side or ray.
 Two adjacent angles can be supplementary or complementary.
Can 2 Adjacent Angles be Supplementary?
Adjacent angles can be defined as two angles that have a common vertex and a common side. The two adjacent angles can be complementary angles or supplementary angles according to the sum of the measurement of angles.
Can Vertical Angles be Adjacent?
No, vertical angles can never be adjacent. Adjacent angles are the two angles next to each other while vertical angles are opposite to each other.
What are Adjacent Angles in Geometry?
Adjacent angles are the two angles that share a common vertex and a common side. The sum of two adjacent angles can be either complementary or supplementary based on their measures.
Give Some Examples of Adjacent Angles in Daily Life?
Steering wheels of the car, open cupboard, three hands of the clock, two pizza slices next to each other in the pizza box. are examples of adjacent angles in daily life.
Can 2 Adjacent Angles Overlap?
No. The angles which are next to each other on one vertex and sharing one side are adjacent angles. Therefore the adjacent angles can not be one on top of the other, or in other words, the angles can not overlap.