Question

vx || su. complete the proof that m∠rtu + m∠xwy = 180°. statement reason 1 vx || su given 2 ∠xwy ≅ ∠utw 3 m∠rtu + m∠utw = 180° angles forming a linear - pair sum to 180° 4 m∠rtu + m∠xwy = 180°

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$, by the corresponding - angles postulate, $\angle XWY\cong\angle UTW$.

Step2: Use linear - pair property

$\angle RTU$ 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:

1. Corresponding - angles postulate; 4. Substitution property of equality.