Definition
Adjacent angles
Adjacent angles share a vertex and one side, and their interiors do not overlap.
Continue from this idea into connected AXIO math.
What it means
Draw three rays from the same point. The two neighboring angles between consecutive rays are adjacent: they meet at the same corner, share the middle ray, and do not lie on top of each other.
Remember it
Angle neighbors: same corner, one shared side, no overlap.
Example
Angles ∠ABC and ∠CBD share vertex B and side BC. If ∠ABC = 32° and ∠CBD = 58°, then the combined angle ∠ABD is 32° + 58° = 90°.
Watch for
Vertical opposite angles share a vertex but not a side, so they are not adjacent.
Common mix-up
Adjacent describes position, not a particular total. Adjacent angles do not have to add to 90° or 180°.
Exact meaning
Two angles are adjacent when they have the same vertex, share exactly one side, and have non-overlapping interiors. Their measures add to the measure of the angle formed by their two unshared sides.