Question

which equation can be used to find the value of x?
x = 45 - 40
x + 45 + 40 = 360
x + 45 + 40 = 180
x = 45 + 40

Explanation:

Step1: Recall Triangle Angle Sum

The sum of interior angles in a triangle is \(180^\circ\). Also, the exterior angle \(x\) and the adjacent interior angle form a linear pair (sum to \(180^\circ\)), but here we can use the exterior angle theorem: an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
The two non - adjacent interior angles to the exterior angle \(x\) are \(45^\circ\) and \(40^\circ\). So by the exterior angle theorem, \(x = 45+40\).
Let's also check the other options:

• Option 1: \(x = 45 - 40\) is incorrect as it does not follow the angle relationships in a triangle.
• Option 2: \(x + 45+40=360\) is incorrect because the sum of angles around a point is \(360^\circ\), but this is not the case here.
• Option 3: \(x + 45 + 40=180\) would be incorrect because \(x\) is an exterior angle, not an interior angle. If we consider the interior angle adjacent to \(x\), let's call it \(y\), then \(y+x = 180\) and \(y + 45+40=180\), so \(x=45 + 40\), not \(x+45 + 40 = 180\).

Step2: Confirm the Correct Equation

From the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So \(x=45 + 40\).

Answer:

\(x = 45+40\) (the fourth option: \(x = 45 + 40\))