Question

which statement regarding the diagram is true?

$m\angle wxy + m\angle xyz = 180^{circ}$

$m\angle wxy + m\angle yxz = 180^{circ}$

$m\angle wxy < m\angle yzx$

$m\angle wxy = m\angle yxz$

Explanation:

Step1: Analyze the angle relationship

Since \(W\), \(X\), and \(Z\) are collinear (they lie on a straight - line), \(\angle WXY\) and \(\angle YXZ\) form a linear pair.

Step2: Use the linear - pair property

By the linear - pair postulate, if two angles form a linear pair, then the sum of their measures is \(180^{\circ}\). So, \(m\angle WXY + m\angle YXZ=180^{\circ}\)

For the first option \(m\angle WXY + m\angle XYZ = 180^{\circ}\), there is no reason from the diagram (angle - addition or linear - pair) to support this. For the third option \(m\angle WXY\lt m\angle YZX\), there is no information about the non - adjacent angles in the triangle to make this comparison. For the fourth option \(m\angle WXY = m\angle YXZ\), unless the ray \(XY\) is a perpendicular bisector (which is not indicated in the diagram), this is not True.

Answer:

\(m\angle WXY + m\angle YXZ = 180^{\circ}\)