Question

1. a. complete the proof that m∠vux + m∠uxy = 180°. statement reason 1 $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$ 2 ∠uxy≅∠suv 3 m∠suv + m∠vux = 180° 4 m∠vux + m∠uxy = 180°

Explanation:

Step1: Given parallel lines

Given that $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$.

Step2: Corresponding - angles postulate

Since $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$, by the corresponding - angles postulate, $\angle UXY\cong\angle SUV$, which means $m\angle UXY = m\angle SUV$.

Step3: Definition of linear pair

$\angle SUV$ and $\angle VUX$ form a linear pair. By the definition of a linear pair of angles, the sum of the measures of two angles in a linear pair is $180^{\circ}$, so $m\angle SUV + m\angle VUX=180^{\circ}$.

Step4: Substitution property

Since $m\angle UXY = m\angle SUV$, we substitute $m\angle UXY$ for $m\angle SUV$ in the equation $m\angle SUV + m\angle VUX = 180^{\circ}$, getting $m\angle VUX + m\angle UXY = 180^{\circ}$.

Answer:

1. Given
2. Corresponding - angles postulate
3. Definition of linear pair
4. Substitution property