Question

complete the proof that m∠sut + m∠wxz = 180°. statement reason 1. wy∥ik given 2. ik∥tv given 3. ∠wxz≅∠ijz corresponding angles theorem 4. m∠ijz + m∠sut = 180° 5. m∠sut + m∠wxz = 180° substitution

Explanation:

Step1: Identify given parallel lines

Given $\overleftrightarrow{WY}\parallel\overleftrightarrow{IK}$ and $\overleftrightarrow{IK}\parallel\overleftrightarrow{TV}$.

Step2: Apply corresponding - angles theorem

Since $\overleftrightarrow{WY}\parallel\overleftrightarrow{IK}$, by the Corresponding Angles Theorem, $\angle WXZ\cong\angle IJZ$, so $m\angle WXZ = m\angle IJZ$.

Step3: Use linear - pair property

$\angle IJZ$ and $\angle SUT$ form a linear pair. By the Linear - Pair Postulate, $m\angle IJZ + m\angle SUT=180^{\circ}$.

Step4: Substitute

Substitute $m\angle WXZ$ for $m\angle IJZ$ in the equation $m\angle IJZ + m\angle SUT = 180^{\circ}$. We get $m\angle SUT + m\angle WXZ=180^{\circ}$.

Answer:

The proof is completed as shown above, using the given parallel - line information, the Corresponding Angles Theorem, the Linear - Pair Postulate, and substitution to show that $m\angle SUT + m\angle WXZ = 180^{\circ}$.