The Angle Addition Postulate

The Angle Addition Postulate states that if two angles share a common side, then the sum of the larger angle is equal to the sum of the two smaller angles.

In this illustration angle ABD is equal to the sum of the smaller angles ABC and CBD.

Here’s another way to represent this postulate. Start by shading in the larger angle, ABD.

Angle ABD is the larger angle and is highlighted red. Now let’s highlight the smaller angles, ABC and CBD.

Combine into one illustration.

With the Angle Addition Postulate, there must be a common side shared by the two smaller angles. There must also be a common vertex shared by all three angles.

When this occurs, the two smaller angles are known as adjacent angles.

Using the Angle Addition Postulate

Example 1. You can use the Angle Addition Postulate to solve a number of geometry and algebra problems. For example, supplementary angles are examples of adjacent angles.

Do you see the common side? Do you see the common vertex?

The measure of the larger angle, ABD, is 180°. Using the Angle Addition Postulate, we get:

You can then solve for an unknown angle using the Angle Addition Postulate.

In this example, x is an unknown angle supplementary to angle CBD. Using the Angle Addition Postulate results in an equation where you can solve for x.

Example 2. You can use the Angle Addition Postulate with other geometric properties to solve problems. For example, take a look at this problem.

Here’s how you can use the Angle Addition Postulate. You know that angle ABC and CBD are supplementary and therefore adjacent. 

Next, we calculate the measure of angle x by noting that the sum of the angle measures of a triangle is 180° and solve for x.