Question

complete the proof that ( mangle sut + mangle wxz = 180^{circ} ).

Explanation:

Step1: Corresponding angles

Since \( \overleftrightarrow{WY}\parallel\overleftrightarrow{FH}\), by the Corresponding Angles Theorem, \( \angle WXZ\cong\angle FGZ\).

Step2: Same - side interior angles

Since \( \overleftrightarrow{FH}\parallel\overleftrightarrow{TV}\), by the Same - Side Interior Angles Theorem, \( m\angle FGZ + m\angle SUT=180^{\circ}\).

Step3: Substitution

Because \( \angle WXZ\cong\angle FGZ\) (so \( m\angle WXZ = m\angle FGZ\)), by substitution, \( m\angle SUT + m\angle WXZ=180^{\circ}\).

Answer:

1. Corresponding Angles Theorem; 4. Same - Side Interior Angles Theorem; 5. Substitution Property of Equality.