Question

list the side lengths of $\triangle def$ in order from shortest to longest.

Explanation:

Step1: Find ∠DFE

$\angle DFE = 180^\circ - 145^\circ = 35^\circ$

Step2: Calculate ∠D

$\angle D = 180^\circ - 70^\circ - 35^\circ = 75^\circ$

Step3: Match sides to angles

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle:

• Smallest angle $\angle DFE=35^\circ$, opposite side $ED$
• Middle angle $\angle E=70^\circ$, opposite side $DF$
• Largest angle $\angle D=75^\circ$, opposite side $EF$

Answer:

$ED < DF < EF$