Adjacent Angles

In the lesson below, you will learn about how to identify whether angles are adjacent.


Adjacent angles are 2 angles that have a common vertex & a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle. The common vertex and common side we mean here are the vertex point and the side which are shared by the 2 angles.

2 angles are Adjacent when they have a common side and a common corner point (vertex) and don’t overlap.

Adjacent Angles

Angle AOB is adjacent to angle BOC


  • they have a common side (line OB)
  • they have a common vertex (point O)

In this diagram, point O is the vertex of all of the angles shown. Angle AOB and angle BOC are adjacent angles because the line OB forms a side of each of those angles.

What Isn’t an Adjacent Angle ?

only share a vertex, not a side NOT Adjacent Angles 1
only share a side, not a vertex NOT Adjacent Angles 2
angles a and b overlap NOT Adjacent Angles 3

Adjacent Angles in Real Life

You can think of adjacent angles as 2 pizza slices next to each other in the box.

  • The corners of the slices are both at the center of the box. that’s where the vertex is.
  • The cut where the slices were separated from one another is the side the angles share.

There are several other pairs of adjacent angles in the whole pizza. Every angle can have 2 possible different angles adjacent to it, one attaching to each side of it. If you have 3 slices of pizza, the middle piece has 2 pieces that are adjacent to it.

Remember! adjacent angles refers to 2 angles at a time.

Learn More

Alternate Exterior Angles

Alternate Interior Angles

Consecutive Interior Angles

Vertical Angles

Geometry Index