Question

complete the proof that \\( \angle vzw \cong \angle xzy \\).

statement	reason
2. \\( m\angle wzx + m\angle xzy = 180^{\circ} \\)
3. \\( m\angle vzw + m\angle wzx = m\angle wzx + m\angle xzy \\)	transitive property of equality
4. \\( m\angle vzw = m\angle xzy \\)	properties of addition, subtraction, multiplication, and division
5. \\( \angle vzw \cong \angle xzy \\)	definition of congruence

Explanation:

Step1: Analyze the reason for statement 2

Since \( \angle WZX\) and \( \angle XZY\) form a linear pair (they are adjacent angles whose non - common sides form a straight line).

Step2: Recall the linear - pair angle sum property

By the property that angles forming a linear pair sum to \(180^{\circ}\).

Answer:

Angles forming a linear pair sum to \(180^{\circ}\)