# Exterior Angle of a Triangle

How to solve the exterior angle of a triangle problems: formula, proof, examples, and their solutions.

## Formula

The measure of an exterior angle (red) of a triangle

is equal to

the sum of the measures of

nonadjacent interior angles of a triangle.

(blue, green)

## Proof

Draw the brown angle.

m∠(blue) + m∠(green) + m∠(brown) = 180

Interior angles of a triangle

m∠(brown) + m∠(red) = 180

Linear pair

The right side of line **1** and **2** are 180.

So m∠(blue) + m∠(green) + m∠(brown)

= m∠(brown) + m∠(red).

To cancel m∠(brown),

write m∠(brown) = m∠(brown),

and do the subtraction.

Then m∠(blue) + m∠(green) = m∠(red)

Switch both sides.

(Symmetric property)

Then m∠(red) = m∠(blue) + m∠(green).

## Example 1

The red angle is the exterior angle of this triangle.

So 10*x* + 7 = 60 + 47.

## Example 2

The red angle is the exterior angle of this triangle.

So 68 = 30 + (7*x* + 3).