Question

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

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 \(\triangle PHO\), \(x\) is an exterior angle. The two non - adjacent interior angles are \(38^{\circ}\) and the other non - adjacent angle (let's call it \(y\)) inside \(\triangle PHO\). So, \(x=38 + y\).
Since \(y>0\) (because it is an angle measure in a triangle, \(y\) represents a positive angle), then \(x>38\).

For the option \(x < 39\): From \(x = 38 + y\), if \(y\geq1\), \(x\geq39\), so this option is wrong.

For the option \(x < 77\): There is no information in the problem (no other angle measures given to suggest a relationship that would make \(x<77\)). If we assume the worst - case scenario for the triangle (but without additional angle info), we can't conclude this.

For the option \(x>103\): There is no basis for this. If we assume the sum of angles in a triangle is \(180^{\circ}\), but we have no information about the third angle of the triangle to support \(x>103\).

Answer:

A. \(x>38\)