Question

question in △def, m∠d = 117° and m∠e = 26°. which list has the sides of △def in order from shortest to longest? answer ef, fd, de fd, ef, de de, fd, ef ef, de, fd fd, de, ef de, ef, fd

Explanation:

Step1: Find angle F

In a triangle, the sum of interior angles is 180°. So, $m\angle F=180^{\circ}-m\angle D - m\angle E=180^{\circ}-117^{\circ}-26^{\circ}=37^{\circ}$.

Step2: Recall 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.
Since $m\angle E < m\angle F < m\angle D$, the sides opposite these angles follow the same order. Side opposite $\angle E$ is $FD$, side opposite $\angle F$ is $DE$, and side opposite $\angle D$ is $EF$.

Answer:

FD, DE, EF