### Exterior Angles

An **Exterior Angle** is the angle formed by one side of a polygon and the extension of the adjacent side.

In all polygons, there are **two** sets of exterior angles, one that goes around clockwise and the other goes around counterclockwise.

Notice that the interior angle and its adjacent exterior angle form a linear pair and add up to

There are two important theorems to know involving exterior angles: the Exterior Angle Sum Theorem and the Exterior Angle Theorem.

The **Exterior Angle Sum Theorem** states that the exterior angles of any polygon will always add up to

The **Exterior Angle Theorem** states that an exterior angle of a triangle is equal to the sum of its remote interior angles. (**Remote Interior Angles** are the two interior angles in a triangle that are not adjacent to the indicated exterior angle.)

What if you knew that two of the exterior angles of a triangle measured

### Examples

#### Example 1

Two interior angles of a triangle are

Remember that every interior angle forms a linear pair (adds up to

So, the measures of the three exterior angles are

#### Example 2

Find the value of

Set up an equation using the Exterior Angle Theorem.

Substitute in

#### Example 3

Find the measure of

Notice that

Set up an equation to solve for the missing angle.

#### Example 4

Find the measures of the numbered interior and exterior angles in the triangle.

We know that

Similarly,

We also know that the three interior angles must add up to

#### Example 5

What is the value of

First, we need to find the missing exterior angle, which we will call

### Review

Determine

Use the following picture for the next three problems:

- What is
m∠1+m∠2+m∠3 ? - What is
m∠4+m∠5+m∠6 ? - What is
m∠7+m∠8+m∠9 ?

Solve for

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.2.

### Resources