Question

complete the proof that m∠rts + m∠vwy = 180°. statement reason 1. vx || su given 2. ∠vwy ≅ ∠stw 3. m∠rts + m∠stw = 180° 4. m∠rts + m∠vwy = 180°

Explanation:

Step1: Identify corresponding - angles

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

Step2: Identify linear - pair angles

$\angle RTS$ and $\angle STW$ 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 $m\angle RTS + m\angle STW=180^{\circ}$.

Step3: Substitute equal - angle measures

Since $\angle VWY\cong\angle STW$, then $m\angle VWY = m\angle STW$. Substituting $m\angle VWY$ for $m\angle STW$ in the equation $m\angle RTS + m\angle STW = 180^{\circ}$, we get $m\angle RTS + m\angle VWY=180^{\circ}$.

Answer:

1. Corresponding - angles postulate; 3. Linear - pair postulate; 4. Substitution property of equality.