Question

which statement about the value of x is true?
o x > 38
o x < 39
o x < 77
o 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 \(\triangle PNO\), the exterior angle at \(N\) is \(x^{\circ}\), and the two non - adjacent interior angles are \(38^{\circ}\) and \(39^{\circ}\).

Step2: Calculate the value of \(x\)

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

Step3: Analyze the inequalities

Since \(x = 77\), we can check each option:

• Option 1: \(x>38\) is true because \(77>38\).
• Option 2: \(x < 39\) is false because \(77>39\).
• Option 3: \(x<77\) is false because \(x = 77\).
• Option 4: \(x>103\) is false because \(77<103\).

Answer:

\(x>38\)