Question

which statement regarding the diagram is true?
○ ( m angle wxy = m angle yxz )
○ ( m angle wxy < m angle yzx )
○ ( m angle wxy + m angle yxz = 180^circ )
○ ( m angle wxy + m angle xyz = 180^circ )

Explanation:

Step1: Analyze the angle relationship

By the definition of a linear pair of angles. A linear pair of angles is formed when two adjacent angles form a straight line. The sum of the measures of angles in a linear pair is \(180^{\circ}\).
In the diagram, \(\angle WXY\) and \(\angle YXZ\) form a linear pair (they are adjacent and their non - common sides form a straight line \(WZ\)).

Answer:

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