Question

In ΔDEF, m∠D = 67° and m∠E = 17°. Which list has the sides of ΔDEF in order from longest to shortest?

Answer 1

In a triangle, the longest side is opposite the largest angle, while the shortest side is opposite the smallest angle.

Step-by-step explanation:

In a triangle, the length of the sides determines the order from longest to shortest. In this case, we are given that the measures of angles D and E are 67° and 17°, respectively.

Since the sum of the angles in a triangle is 180°, we can find the measure of angle F by subtracting the sum of angles D and E from 180°. So, angle F = 180° - 67° - 17° = 96°.

Now, we can determine the order of the sides. The angle opposite the longest side is the largest angle, so side DE is the longest side.

Since angle D is greater than angle F, side DF is the second longest side. And finally, side EF is the shortest side.