1. The problem asks: Which angles are congruent to $\angle 2$? - $\angle 2$ is an alternate interior angle with $\angle 6$ (because lines $m$ and $n$ are parallel and cut by the transversal). - $\angle 3$ is vertically opposite to $\angle 2$, so they are congruent. - $\angle 7$ is corresponding to $\angle 3$; since $\angle 3$ is congruent to $\angle 2$, $\angle 7$ is also congruent to $\angle 2$. Thus, the angles congruent to $\angle 2$ are $\angle 3$, $\angle 6$, and $\angle 7$. 2. The problem asks: Which postulate or theorem justifies that $\angle 1$ is congruent to $\angle 5$? - $\angle 1$ and $\angle 5$ are corresponding angles formed by the transversal cutting lines $m$ and $p$. - According to the Corresponding Angles Postulate, when lines are parallel, corresponding angles are congruent. Therefore, the correct justification is the Corresponding Angles Postulate. 3. The problem asks: Which postulate or theorem justifies that $\angle 4$ is supplementary to $\angle 7$? - $\angle 4$ and $\angle 7$ are consecutive interior angles between lines $m$ and $n$ and the transversal. - Consecutive Interior Angles Theorem states that consecutive interior angles are supplementary. Therefore, the justification is the Consecutive Interior Angles Theorem. 4. The problem asks: Are $\angle 4$, $\angle 6$, $\angle 8$ supplementary to $\angle 7$? True or False? - Supplementary angles sum to $180^\circ$. - $\angle 4$ and $\angle 7$ are consecutive interior angles and are supplementary. - $\angle 6$ and $\angle 7$ are not supplementary; they are alternate interior angles and thus congruent. - $\angle 8$ and $\angle 7$ are adjacent angles on line $n$ and sum to $180^\circ$, so supplementary. Therefore, the statement is False because $\angle 6$ is not supplementary to $\angle 7$. Correction: $\angle 4$ and $\angle 8$ are supplementary to $\angle 7$, but $\angle 6$ is congruent, not supplementary. 5. The problem asks: Does the Alternate Interior Angles Theorem justify that $\angle 3$ is congruent to $\angle 5$? True or False? - $\angle 3$ and $\angle 5$ lie between different pairs of lines ($m-n$ and $n-p$ respectively), so this theorem does not apply. - Alternate Interior Angles Theorem applies between two parallel lines and a transversal. Therefore, the statement is False. Correction: $\angle 3$ is congruent to $\angle 5$ because of the Corresponding Angles Postulate if the lines involved are parallel. 6. The problem asks: Does the Consecutive Exterior Angles Theorem justify that $\angle 2$ is supplementary to $\angle 5$? True or False? - $\angle 2$ and $\angle 5$ are not consecutive exterior angles; $\angle 2$ is interior while $\angle 5$ is exterior. Therefore, the statement is False. Correction: $\angle 2$ is congruent to $\angle 6$ (Alternate Interior Angles), and $\angle 5$ pairs with $\angle 1$ as corresponding angles, but $\angle 2$ and $\angle 5$ are neither supplementary nor justified by Consecutive Exterior Angles Theorem.