Question

complete the proof that m∠xwy + m∠rtu = 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∠xwy + m∠rtu = 180°

Explanation:

Step1: Identify angle - relationship

Since $\overrightarrow{VX}\parallel\overrightarrow{SU}$, $\angle XWY$ and $\angle UTW$ are alternate - interior angles. Alternate - interior angles formed by parallel lines are congruent.

Step2: Substitute equal angles

We know that $\angle XWY\cong\angle UTW$, so $m\angle XWY = m\angle UTW$. Given that $m\angle RTU+m\angle UTW = 180^{\circ}$ (angles forming a linear pair sum to $180^{\circ}$), by substituting $m\angle XWY$ for $m\angle UTW$, we get $m\angle XWY + m\angle RTU=180^{\circ}$.

Answer:

1. Reason: Alternate - interior angles of parallel lines are congruent.
2. Reason: Substitution property of equality.