In geometry, we give different names to different types of angles depending on the measure of the given angle: right angles, adjacent supplementary angles, vertical angles. But how do we know which is which?
Let’s start with the basics.
If the measure of the angle is exactly 90 degrees, it’s known as a right angle. If an angle is less than 90 degrees, it’s an acute angle. An angle greater than 90 degrees is an obtuse angle. If the measure of an angle is equal to 180 degrees, it’s known as a straight angle.
There are also names given to pairs of angles.
Vertical angles, or opposite angles, are the two angles directly opposite each other when two straight lines cross (Figure 1).
Complementary angles are two angles that add to 90 degrees (Figure 2).
Supplementary angles are two angles that add up to 180 degrees (Figure 3).
Adjacent Angles vs. Nonadjacent Angles
Angles are adjacent when they share a common side and a common vertex.
Angles 1 and 2 are nonadjacent, while angles 3 and 4 are — they share a common side and vertex.
Adjacent Supplementary Angles Defined
Now that we understand the definitions of adjacent and nonadjacent angles, we can see that adjacent supplementary angles are two angles that share a side and vertex and add up to 180 degrees.
Using this definition, look at the diagram below to see which angles are adjacent supplementary.
Angles ABC and ABD are adjacent because they share line segment AB and vertex B.
Angles EFG and HIJ are not adjacent because they don’t share any common side.
However, the angle measures in both pairs of supplementary angles (ABC and ABD, and EFG and HIJ) still equal 180 degrees.
To review, that means EFG and HIJ are supplementary angles. However, only ABC and ABD are adjacent supplementary angles.
Recognizing Adjacent Supplementary Angles
To recap, adjacent supplementary angles don’t just share a side and vertex but they also add up to 180 degrees. These angles commonly show up in geometry proofs, so if you’re not sure, look for a straight line intersected by another line segment with the two angles sharing a common side and vertex.