Grade 7 geometry lesson
Adjacent Angles: Definition, Examples, Chart, and Practice
Adjacent angles are two angles that sit next to each other. They share a vertex and one side, but their inside regions do not overlap.
What are adjacent angles?
Adjacent angles are two angles that are next to each other.
They share the same vertex. They also share one side, called the common side.
The two angle spaces do not overlap. They touch along the common side, but one angle does not cover the other.
Adjacent angles rule
Use these three checks when you decide whether two angles are adjacent.
Adjacent angles share a vertex, share one side, and do not overlap.
If any one of those checks is missing, the angles are not adjacent.
Adjacent angles chart
The chart shows what to check in a diagram.
Adjacent angles can be small, large, or part of a straight line. The main idea is that they sit side by side.
How to identify adjacent angles
Step 1: Find the vertex of each angle.
Step 2: Check whether the two angles share the same vertex.
Step 3: Check whether they share exactly one side.
Step 4: Check that the two angle spaces do not overlap.
Worked example
Problem: Angle A is 38° and angle B is 61°. They share a vertex and one side, and they do not overlap. Are they adjacent?
Answer: Yes. The measures do not decide adjacency. The position decides it.
The two angles are adjacent because they sit side by side with one common side.
Adjacent angles on a straight line
Some adjacent angles form a straight angle.
When that happens, their measures add to 180°, so they are also supplementary angles.
Example: If one angle is 74° and the adjacent angle completes a straight line, the other angle is 180° - 74° = 106°.
Common mistakes
Do not call angles adjacent just because they are near each other. They must share a vertex and one side.
Do not choose angles that overlap. Adjacent angles touch along a side but do not cover the same space.
Do not assume all adjacent angles add to 180°. They add to 180° only when they make a straight line, and they are different from vertical angles, which sit opposite each other.
Quick practice
1. Two angles share a vertex and one side. They do not overlap. They are adjacent.
2. Two angles are opposite each other when lines cross. They are vertical angles, not adjacent angles.
3. Two adjacent angles make a straight line. One is 49°. The other is 131°.
4. Two angles are close together but have different vertices. They are not adjacent.
Interactive playground
Split a straight angle
Move the shared side. The two angles stay adjacent because they share a vertex, share one side, and do not overlap.