Question

which statement about the value of ( x ) is true?
( x < 39 )
( x > 38 )
( x > 103 )
( x < 77 )

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(PON\), \(x\) is an exterior angle. The two non - adjacent interior angles are \(38^{\circ}\) and \(39^{\circ}\). But wait, actually, the exterior angle \(x\) is greater than either of the non - adjacent interior angles.

Step2: Compare \(x\) with the non - adjacent interior angle

Since \(x\) is an exterior angle of the triangle and one of the non - adjacent interior angles is \(38^{\circ}\), by the exterior angle theorem (exterior angle \(>\) non - adjacent interior angle), we have \(x>38\).

Answer:

\(x > 38\)