Question

in $\triangle lmn$, $mangle l = 35^{circ}$ and $mangle m = 78^{circ}$. which list has the sides of $\triangle lmn$ in order from longest to shortest? answer attempt 1 out of 2 lm, mn, nl nl, lm, mn lm, nl, mn nl, mn, lm mn, nl, lm mn, lm, nl

Explanation:

Step1: Find the measure of angle N.

The sum of angles in a triangle is 180°. So, $m\angle N=180-(m\angle L + m\angle M)=180-(35 + 78)=67^{\circ}$.

Step2: Recall the angle - side relationship in a triangle.

In a triangle, the side opposite the largest angle is the longest and the side opposite the smallest angle is the shortest.
Since $78^{\circ}(m\angle M)>67^{\circ}(m\angle N)>35^{\circ}(m\angle L)$, the side opposite $\angle M$ (NL), is the longest, the side opposite $\angle N$ (LM) is the second - longest, and the side opposite $\angle L$ (MN) is the shortest.

Answer:

NL, LM, MN