Question - Lines and Angles
Solution:
The diagram shows two lines, line $$ l $$ and line $$ m $$, cut by a transversal line $$ r $$. According to the information provided, $$ m\angle2 = m\angle7 $$. Angles 2 and 7 are alternate exterior angles. If the measures of alternate exterior angles are equal, then by the Converse of the Alternate Exterior Angles Theorem, the lines are parallel.So, the correct answer is:D) $$ l \parallel m $$, by the Converse of the Same-Side Interior Angles Postulate.However, please be aware there's an inconsistency between the answer and the justification in the options provided. Answer D incorrectly states "Same-Side Interior Angles Postulate" as the justification, when it should be "Alternate Exterior Angles Theorem" for the reason discussed.
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