Question

order the side lengths $cd$, $de$, and $ec$ from least to greatest.
(note that the figure is not drawn to scale.)
$square < square < square$

Explanation:

Step1: Calculate ∠D

The sum of angles in a triangle is $180^\circ$.
$\angle D = 180^\circ - 85^\circ - 42^\circ = 53^\circ$

Step2: Match sides to opposite angles

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

• Side $CD$ is opposite $\angle E = 85^\circ$
• Side $DE$ is opposite $\angle C = 42^\circ$
• Side $EC$ is opposite $\angle D = 53^\circ$

Step3: Order sides by angle size

Sort angles from smallest to largest: $42^\circ < 53^\circ < 85^\circ$. Match to their opposite sides.

Answer:

$DE < EC < CD$