Question

question in △lmn, mn = 18, nl = 15, and lm = 4. which statement about the angles of △lmn must be true? answer m∠m > m∠n > m∠l m∠l > m∠n > m∠m m∠l > m∠m > m∠n m∠n > m∠m > m∠l m∠m > m∠l > m∠n m∠n > m∠l > m∠m

Explanation:

Step1: Recall angle - side relationship in a triangle

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

Step2: Identify the opposite angles to the given sides

Side $MN = 18$ is opposite $\angle L$, side $NL=15$ is opposite $\angle M$, and side $LM = 4$ is opposite $\angle N$.

Step3: Compare the side lengths

We have $MN>NL > LM$, i.e., $18>15 > 4$.

Step4: Determine the angle - size relationship

Since the larger side has the larger opposite - angle, we have $m\angle L>m\angle M>m\angle N$.

Answer:

m∠L > m∠M > m∠N