Question

lines $overleftrightarrow{hn}$ and $overleftrightarrow{km}$ are shown with the transversal line $overleftrightarrow{gl}$. which statements would prove the lines are parallel? $angle ghicongangle ihj$ $angle ghicongangle kjh$ $mangle mjh + mangle nhj=180^{circ}$ $mangle kjh + mangle kjl = 180^{circ}$ $angle ghicongangle nhj$ $angle ghicongangle mjl$ $mangle kjh + mangle ihj = 180^{circ}$

Explanation:

Step1: Recall parallel - line angle relationships

When two lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary for the lines to be parallel.

Step2: Analyze each option

• $\angle GHI$ and $\angle IHJ$ are adjacent angles, not related to parallel - line properties.
• $\angle GHI$ and $\angle KJH$ are corresponding angles. If $\angle GHI\cong\angle KJH$, then $\overleftrightarrow{HN}\parallel\overleftrightarrow{KM}$ by the corresponding - angles postulate.
• $\angle MJH$ and $\angle NHJ$ are vertical angles, not related to parallel - line properties.
• $\angle KJH$ and $\angle KJL$ are adjacent angles, not related to parallel - line properties.
• $\angle GHI$ and $\angle NHJ$ are vertical angles, not related to parallel - line properties.
• $\angle GHI$ and $\angle MJL$ are not related in a way that proves parallel lines.
• $\angle KJH$ and $\angle IHJ$ are same - side interior angles. If $m\angle KJH + m\angle IHJ=180^{\circ}$, then $\overleftrightarrow{HN}\parallel\overleftrightarrow{KM}$ by the same - side interior angles postulate.

Answer:

$\angle GHI\cong\angle KJH$, $m\angle KJH + m\angle IHJ = 180^{\circ}$