Question

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which equation can you use to find the value of x?
$x = 120 + 35$
$x = 120 - 35$
$x + 120 + 35 = 180$
$x + 120 - 35 = 180$

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. But here, we can also use the angle - sum property of a triangle. The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third interior angle of the triangle (not labeled) be \(y\). Then \(y + 120+35 = 180\) (angle - sum property of a triangle). Also, \(x\) and \(y\) are supplementary angles (\(x + y=180\)). Substituting \(y = 180-(120 + 35)\) into \(x + y=180\) gives \(x=120 + 35\).

Answer:

\(x = 120+35\)