Given the following information, determine which lines, if any, are parallel. State the theorem that justifies your answer.
5. $\angle 1 \cong \angle 6$
6. $m \angle 7+m \angle 6=180^{\circ}$

Answer

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Answer

\boxed{\text{The lines are parallel, justified by the Converse of the Alternate Interior Angles Theorem}}

Steps

Step 1 ：Given: $\angle 1 \cong \angle 6$ and $m \angle 7 + m \angle 6 = 180^\circ$

Step 2 ：Since $\angle 1 \cong \angle 6$, check if they are alternate interior angles

Step 3 ：If the sum of the measures of angles 1 and 6 is equal to 180 degrees, then they are alternate interior angles and the lines are parallel

Step 4 ：$2m \angle 1 = 180^\circ$

Step 5 ：\boxed{\text{The lines are parallel, justified by the Converse of the Alternate Interior Angles Theorem}}