Question

tv || pr and pr || wy. complete the proof that m∠wxz + m∠sut = 180°. statement reason 1 tv || pr 2 pr || wy 3 ∠wxz ≅ ∠pqz 4 m∠pqz + m∠sut = 180° 5 m∠wxz + m∠sut = 180°

Explanation:

Step1: Given

Given

Step2: Given

Given

Step3: Corresponding - angles postulate

Since $\overleftrightarrow{PR}\parallel\overleftrightarrow{WY}$, corresponding - angles are congruent.

Step4: Same - side interior angles postulate

Since $\overleftrightarrow{TV}\parallel\overleftrightarrow{PR}$, same - side interior angles are supplementary.

Step5: Substitution property of equality

Since $\angle WXZ\cong\angle PQZ$, we can substitute $\angle WXZ$ for $\angle PQZ$ in the equation $m\angle PQZ + m\angle SUT=180^{\circ}$.

Answer:

1. Given
2. Given
3. Corresponding - angles postulate
4. Same - side interior angles postulate
5. Substitution property of equality