Question

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

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle PNO\), \(\angle PNM\) (where \(\angle PNM=x^{\circ}\)) is an exterior angle. The two non - adjacent interior angles are \(\angle NPO\) and \(\angle NOP\).

Step2: Calculate the value of \(x\)

By the exterior - angle property of a triangle, \(x = 38+39\).
\[x=77\]

Step3: Analyze the inequalities

Since \(x = 77\), \(x>38\) is true because \(77>38\), \(x<39\) is false because \(77>39\), \(x < 77\) is false because \(x = 77\), and \(x>103\) is false because \(77<103\).

Answer:

\(x>38\)