Okay, here’s a brain zinger: if someone tells you that they are using the **awesome Angle Addition Postulate**, what do you think they are **adding**?

If you said “**angles,”** you would be 100 percent correct!

The Angle Addition Postulate basically means we are taking two angles and joining them together to make one LARGER angle!

Here’s a basic example”

We’ll take ∠GEM and ∠MEO

- Let’s join them together do that the angle converges at point E.
- We’ll also lay them together so that the two angles share the same border EM.

What can we do with the **Angle Addition Postulate**?

Great question!

Let’s look at the above angle again. If ∠GEO was 125°, then what is ∠GEM?

Even without geometry help from an online math tutor, it’s almost like slicing a piece of cake!

∠GEM + ∠MEO = ∠GEO

∠GEM + ∠MEO = 125°

We know that ∠MEO = 90° because it is a right angle with the little square.

∠GEM+ ∠90° = 125°

∠GEM = 35°

Let’s go for something harder:

What are the angles below?

Easy!

First of all, we know that ∠ABD and ∠DBC follow the Angle Addition Postulate. This is because they share the same vertex at point B. The two angles share the same line BD, so they line up.

∠ABD + ∠DBC = ∠ABC

We know that AC is a *straight line*, and *straight angles are 180°*

We also have the formulas for ∠ABD and ∠DBC

Let’s plug ‘em in:

∠ABD + ∠DBC = ∠ABC

(5x+10) + (2x-5) = 180°

5x + 10 + 2x – 5 = 180

7x + 5 = 180

7x = 175

x = 25

So, now that we know what is, we can plug it into the original formulas! ∠ABD = 5x + 10, x = 25

**∠ABD=135°**

∠DBC = 2x – 5, x = 25

**∠ABD=45°**

Let’s check:

∠ABD + ∠DBC = ∠ABC

We are balanced!

For more on how to use the half-angle formula.