Question

which equation can be used to find the value of x?
$x = 60 - 40$
$x + 40 + 60 = 360$
$x + 40 + 60 = 180$
$x = 60 + 40$
(image of a triangle with angles 40°, 60°, and an exterior angle x°)

Explanation:

Step1: Recall triangle exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the given triangle, the exterior angle is \(x\), and the two non - adjacent interior angles are \(40^{\circ}\) and \(60^{\circ}\). So, by the exterior angle theorem, we have the equation \(x = 60 + 40\).

Step2: Analyze other options

• For \(x=60 - 40\): This would imply that the exterior angle is the difference of the two interior angles, which is not in line with the exterior angle theorem.
• For \(x + 40+60=180\): The sum of an exterior angle and the adjacent interior angle is \(180^{\circ}\) (linear pair), but here \(x\) is an exterior angle, and \(40^{\circ}\) and \(60^{\circ}\) are non - adjacent interior angles. The sum \(x + 40+60\) is not equal to \(180^{\circ}\).
• For \(x + 40+60 = 360\): The sum of angles around a point is \(360^{\circ}\), but this is not the case here as we are dealing with a triangle's exterior angle.

Answer:

\(x = 60 + 40\) (the fourth option in the given set of equations)