Question

eg || rt and eg || uw. complete the proof that m∠uvx + m∠qsr = 180°. statement reason 1 eg || rt 2 eg || uw 3 ∠qsr ≅ ∠efq 4 m∠efq + m∠uvx = 180° 5 m∠uvx + m∠qsr = 180°

Explanation:

Step1: Given information

Given $\overrightarrow{EG}\parallel\overrightarrow{RT}$ and $\overrightarrow{EG}\parallel\overrightarrow{UW}$

Step2: Corresponding - angles property

Since $\overrightarrow{EG}\parallel\overrightarrow{RT}$, $\angle QSR\cong\angle EFQ$ (Corresponding - angles postulate: When two parallel lines are cut by a transversal, corresponding angles are congruent)

Step3: Same - side interior angles property

Since $\overrightarrow{EG}\parallel\overrightarrow{UW}$, $\angle EFQ$ and $\angle UVX$ are same - side interior angles. So, $m\angle EFQ + m\angle UVX=180^{\circ}$ (Same - side interior angles postulate: When two parallel lines are cut by a transversal, same - side interior angles are supplementary)

Step4: Substitution property

Since $\angle QSR\cong\angle EFQ$, we can substitute $\angle QSR$ for $\angle EFQ$ in the equation $m\angle EFQ + m\angle UVX = 180^{\circ}$. So, $m\angle UVX + m\angle QSR=180^{\circ}$

Answer:

1. Given
2. Given
3. Corresponding - angles postulate
4. Same - side interior angles postulate
5. Substitution property