Question

which statement regarding the diagram is true?
( m angle w x y=m angle y x z )
( m angle w x y<m angle y z x )
( m angle w x y+m angle y x z=180^{circ} )
( m angle w x y+m angle x y z=180^{circ} )

Explanation:

Step1: Analyze the angle - relationship

We know that \(\angle WXY\) and \(\angle YXZ\) form a linear pair. By the definition of a linear pair of angles, if two adjacent angles form a straight line, then the sum of their measures is \(180^{\circ}\).

Step2: Check each option

• Option 1: \(\angle WXY\) and \(\angle YXZ\) are not necessarily equal. There is no information in the diagram to suggest they are congruent.
• Option 2: There is no basis from the given diagram to conclude that \(m\angle WXY
• Option 3: Since \(\angle WXY\) and \(\angle YXZ\) are adjacent and form a straight line (\(\angle WXZ\) is a straight angle with measure \(180^{\circ}\)), by the linear - pair postulate \(m\angle WXY + m\angle YXZ=180^{\circ}\).
• Option 4: \(\angle WXY\) and \(\angle XYZ\) are not adjacent to form a straight line. The sum of angles in a triangle \( \triangle XYZ\) is \(m\angle YXZ + m\angle XYZ+m\angle Y = 180^{\circ}\), not \(m\angle WXY + m\angle XYZ\).

Answer:

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