Question

in $\triangle efg$, $mangle e = 107^{circ}$ and $mangle v = 51^{circ}$. which list has the sides of $\triangle efg$ in order from shortest to longest? answer:
options:
ge, ef, fg
fg, ef, ge
fg, ge, ef
ef, fg, ge
ge, fg, ef
ef, ge, fg

Explanation:

Step1: Find the third - angle measure

The sum of the interior angles of a triangle is 180°. Let the third angle be $\angle G$. So, $m\angle E+m\angle V + m\angle G=180^{\circ}$. Given $m\angle E = 107^{\circ}$ and $m\angle V=51^{\circ}$, then $m\angle G=180-(107 + 51)=22^{\circ}$.

Step2: Recall the angle - side relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest. The smallest angle is $\angle G = 22^{\circ}$, the side opposite it is $EV$. The middle - sized angle is $\angle V=51^{\circ}$, the side opposite it is $GE$. The largest angle is $\angle E = 107^{\circ}$, the side opposite it is $VG$.

Answer:

EV, GE, VG