Question

in △def, m∠d = 67° and m∠e = 17°. which list has the sides of △def in order from longest to shortest? answer: fd, de, ef; de, fd, ef; de, ef, fd; ef, fd, de; ef, de, fd; fd, ef, de

Explanation:

Step1: Find angle F

In a triangle, the sum of interior angles is 180°. So, $m\angle F=180^{\circ}-m\angle D - m\angle E=180^{\circ}-67^{\circ}-17^{\circ}=96^{\circ}$.

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.
The largest angle is $\angle F = 96^{\circ}$, opposite side is $DE$. The second - largest angle is $\angle D=67^{\circ}$, opposite side is $EF$. The smallest angle is $\angle E = 17^{\circ}$, opposite side is $FD$.

Answer:

DE, EF, FD