Question

in $\triangle def$, $mangle d = 83^{circ}$ and $mangle e = 30^{circ}$. which list has the sides of $\triangle def$ in order from longest to shortest? answer
○ de, ef, fd
○ fd, de, ef
○ fd, ef, de
○ ef, de, fd
○ ef, fd, de
○ de, fd, ef

Explanation:

Step1: Find angle F

In a triangle, the sum of interior angles is 180°. So, $m\angle F=180^{\circ}-m\angle D - m\angle E=180^{\circ}-83^{\circ}-30^{\circ}=67^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. Since $m\angle D = 83^{\circ}$, $m\angle F=67^{\circ}$, $m\angle E = 30^{\circ}$, and the side opposite $\angle D$ is $EF$, the side opposite $\angle F$ is $DE$, and the side opposite $\angle E$ is $FD$.

Answer:

EF, DE, FD