Adjacent Angles – Definition, Meaning, Properties, Examples

What Are Adjacent Angles?

Adjacent angles are two angles that have a common side and a common vertex but do not overlap. Essentially, they are angles that sit next to each other, sharing one side. The sum of the measures of adjacent angles always equals the measure of the angle formed by the non-shared sides. To identify adjacent angles, look for two angles with a shared side and vertex.

For instance, if you have angles ∠ABC and ∠CBD, where the common side is BC and the common vertex is B, these angles are considered adjacent.

Properties of Adjacent Angles

Adjacent angles share a side and a vertex. If their non-common sides form a straight line, they’re a linear pair with a sum of \(180^\circ\). The total angle formed by non-shared sides equals the sum of their measures. The common side can act as a bisector, but the angles aren’t necessarily equal.

How to Identify Adjacent Angles

  1. Look for Shared Side: Find two angles that share a side.
  2. Check for Shared Vertex: Ensure these angles also share a common corner or point (vertex).
  3. No Overlapping: Confirm that the angles don’t overlap; they should be side by side.
  4. Straight Line Check: If the sides of the angles, excluding the shared one, form a straight line, then the angles are adjacent.

Remember, adjacent angles are like neighbors that share a fence (common side) and a meeting point (common vertex).

Identify Adjacent Angles

In this diagram:

  • ∠ABC and ∠BCA are adjacent angles because they share the common side BC and the common vertex B.
  • ∠ABC and ∠CBD are not adjacent angles because they share a common side (BC), but they do not share a common vertex.

So, in simple terms, ∠ABC and ∠BCA are adjacent because they are side by side and share a common side and vertex.