Question

in △lmn, mn = 8, nl = 13, and lm = 9. which statement about the angles of △lmn must be true? answer m∠l > m∠n > m∠m m∠l > m∠m > m∠n m∠n > m∠m > m∠l m∠n > m∠l > m∠m m∠m > m∠l > m∠n m∠m > m∠n > m∠l

Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the side length, the larger the measure of the opposite angle.

Step2: Identify opposite angles

In \(\triangle LMN\), side \(NL = 13\) is opposite \(\angle M\), side \(LM=9\) is opposite \(\angle N\), and side \(MN = 8\) is opposite \(\angle L\).

Step3: Compare side lengths

We have \(NL>LM > MN\).

Step4: Determine angle - size order

Since \(NL\) is the longest side, \(\angle M\) is the largest angle. Since \(LM\) is the second - longest side, \(\angle N\) is the second - largest angle. Since \(MN\) is the shortest side, \(\angle L\) is the smallest angle. So \(m\angle M>m\angle N > m\angle L\).

Answer:

\(m\angle M>m\angle N > m\angle L\) (the option that matches this relationship among the given choices)