1. Supplementary Angles
Supplementary angles are adjacent angles which add up to 180 degrees (or π radians) when combined. Supplementary angles are simple to identify visually because because they will all intersect at a line segment which cuts straight across.
Another way to think of it is that a perfectly straight angle on a piece of paper, such as the radius of a circle, will always have a value of 180 degrees. Therefore, any adjacent angles contained within that 180 degree sweep will necessarily have to add up to 180.
2. Complementary Angles
Complementary angles are very similar to supplementary angles but add up to 90 degrees instead of 180. As such, these adjacent angles must be contained within a “square” angle of 90 degrees (.5π radians).
Complementary angles can be a bit trickier to identify visually because values like 92 degrees or 88 degrees may still look square to the naked eye.
Generally, while doing geometry problems, your instructor or textbook writer will include an indicator to show when an angle is exactly 90 degrees. In many textbooks, as well as engineering documents, 90-degree corners are called out using a small square icon (rather than a curved arc) inside the angle.
3. Vertical Angles
Vertical angles can be thought of as two sets of supplementary angles which are considered adjacent angles to each other. Therefore, they add up to a full 360 degrees (2π radians).
To identify vertical angles visually, you can try drawing a full circle around them with a compass. If the circle is able to connect with every segment, you’re probably dealing with vertical angles.
The simplest vertical angles are just two lines which intersect straight through each other, creating four linear pairs of discrete angles which add up to 360.
Any number of angles can be added inside these segments, complicating the calculation process. However, the sum will always be 360 no matter how many adjacent angles are involved.
Other Adjacent Angles Examples
Supplementary angles, complementary angles and vertical angles are all useful in studying geometry because they can be identified visually by the student or worker.
However, there is no rule stating that adjacent angles have to fit into those three categories. These examples of adjacent angles will add up to values other than 90, 180 or 360 degrees.
Generally, if you are required to calculate other types of adjacent angles, your instructor or textbook will tell you the total sum so that you can use that value to calculate any unknown angles. Otherwise, you’ll need a manual tool such as a protractor to measure the exact value.
