The Exterior Angle Theorem Made Easy

The Exterior Angle Theorem is a key idea to help us learn about triangles.

In simple terms, it tells us that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. This idea is interesting and helps us understand different properties of triangles.

What is the Theorem?

Let's look at a triangle called ( ABC ).

If we take one of its sides, like ( BC ), and stretch it out to a new point ( D ), the angle formed at ( D ), which we call ( \angle ACD ), becomes an exterior angle.

According to the Exterior Angle Theorem, we can write this like this:

$$\angle ACD = \angle A + \angle B$$

Here, ( \angle A ) and ( \angle B ) are the two angles inside the triangle that are not next to ( \angle ACD ).

A Simple Example

Imagine we have triangle ( ABC ) where:

• ( \angle A = 40^\circ )
• ( \angle B = 70^\circ )

Now, using the Exterior Angle Theorem, we can find ( \angle ACD ):

$$\angle ACD = 40^\circ + 70^\circ = 110^\circ$$

Quick Recap

1. The exterior angle is the total of the two opposite interior angles.
2. This theorem reminds us that all angles inside a triangle always add up to ( 180^\circ ).

Understanding this helps with solving problems and makes learning about triangles even more fun!