Triangle: Exterior Angle

How to solve the exterior angle of a triangle: formula, 2 examples, and their solutions.

Formula

Formula

m∠1 = m∠2 + m∠3

m∠1: Exterior angle of a triangle
m∠2, m∠3: Non-adjacent interior angles

Example 1

Example

Solution

The measure of the exterior angle is
[10x + 7].

The measures of the non-adjacent interior angles are
[60] and [47].

So [10x + 7] = [60] + [47].

60 + 47 = 107

Subtract 7 from both sides.

Then 10x = 100.

Divide both sides by 10.

Then x = 10.

So x = 10.

Example 2

Example

Solution

The measure of the exterior angle is
[68].

The measures of the non-adjacent interior angles are
[30] and [7x + 3].

So [30] + [7x + 3] = [68].

30 + 3 = +33

Move +33 to the right side.

Then 7x = 35.

Divide both sides by 7.

Then x = 5.

So x = 5.