Question

su || vx. complete the proof that m∠rtu + m∠xwy = 180°. statement reason 1 su || vx given 2 ∠xwy ≅ ∠utw 3 m∠rtu + m∠utw = 180° 4 m∠rtu + m∠xwy = 180°

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$, $\angle XWY$ and $\angle UTW$ are corresponding angles, so $\angle XWY\cong\angle UTW$ (corresponding - angles postulate).

Step2: Recognize linear - pair

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

Step3: Substitute equal angles

Since $\angle XWY\cong\angle UTW$, then $m\angle XWY = m\angle UTW$. Substituting $m\angle XWY$ for $m\angle UTW$ in the equation $m\angle RTU + m\angle UTW = 180^{\circ}$, we get $m\angle RTU + m\angle XWY=180^{\circ}$.

Answer:

The reasons for statements 2, 3, and 4 are:

1. Corresponding - angles postulate
2. Linear - pair postulate
3. Substitution property of equality