Question

question 3
1 pts
which statement proves that x||y?
∠6≅∠9
∠14 is supplementary to ∠15.
∠2 is supplementary to ∠3.
∠12≅∠13
for exercises 4 - 6, use the figure at the right.

Explanation:

Step1: Recall parallel - line angle rules

If two lines are parallel, corresponding angles are congruent, alternate - interior angles are congruent, and same - side interior angles are supplementary.

Step2: Analyze each option

• $\angle6$ and $\angle9$ are not corresponding, alternate - interior, or same - side interior angles for lines $x$ and $y$, so $\angle6\cong\angle9$ does not prove $x\parallel y$.
• $\angle14$ and $\angle15$ are same - side interior angles for lines that are not $x$ and $y$, so $\angle14$ being supplementary to $\angle15$ does not prove $x\parallel y$.
• $\angle2$ and $\angle3$ are same - side interior angles for lines $x$ and $y$. If $\angle2$ is supplementary to $\angle3$ (i.e., $m\angle2 + m\angle3=180^{\circ}$), then by the same - side interior angles postulate, $x\parallel y$.
• $\angle12$ and $\angle13$ are not corresponding, alternate - interior, or same - side interior angles for lines $x$ and $y$, so $\angle12\cong\angle13$ does not prove $x\parallel y$.

Answer:

$\angle2$ is supplementary to $\angle3$