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 \(x\) is equal to the sum of the two non - adjacent interior angles.

Step2: Analyze Each Option

• Option 1: \(x = 45 - 40\) is incorrect. The exterior angle is the sum, not the difference, of the non - adjacent interior angles.
• Option 2: \(x + 45+40 = 360\) is incorrect. The sum of angles around a point is \(360^\circ\), but here we are dealing with a triangle's exterior angle and interior angles.
• Option 3: \(x + 45 + 40=180\) is incorrect. The sum of the interior angles of a triangle is \(180^\circ\), but \(x\) is an exterior angle.
• Option 4: By the exterior angle theorem, an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So \(x=45 + 40\).

Answer:

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