Question

line - segment rm is parallel to nd with transversal wk, as shown. an incomplete proof is shown. given: rm||nd and wk is a transversal prove: ∠wgm and ∠khd are supplementary statement reason 1. rm||nd and wk is a transversal 1. given 2. m∠wgm + m∠hgm = 180° 2. if two angles form a linear - pair, then they are supplementary. 3. ∠hgm≅∠khd 3. 4. m∠hgm = m∠khd 4. 5. m∠wgm + m∠khd = 180° 5. 6. ∠wgm and ∠khd are supplementary 6. definition of supplementary angles.

Explanation:

Step1: Recall corresponding - angles postulate

Since $\overline{RM}\parallel\overline{ND}$ and $\overline{WK}$ is a transversal, $\angle HGM$ and $\angle KHD$ are corresponding angles. So, $\angle HGM\cong\angle KHD$ by the Corresponding - Angles Postulate.

Step2: Use the property of congruent angles

If two angles are congruent, their measures are equal. So, if $\angle HGM\cong\angle KHD$, then $m\angle HGM = m\angle KHD$ by the Definition of Congruent Angles.

Step3: Substitute equal - measure angles

We know that $m\angle WGM+m\angle HGM = 180^{\circ}$ (from the linear - pair property). Substituting $m\angle HGM$ with $m\angle KHD$ (since $m\angle HGM = m\angle KHD$), we get $m\angle WGM + m\angle KHD=180^{\circ}$.

Answer:

1. Corresponding - Angles Postulate; 4. Definition of Congruent Angles; 5. Substitution Property of Equality