Question

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

Explanation:

Step1: Find ∠UXV

∠UXV and ∠UXW are supplementary, so:
$\angle UXV = 180^\circ - 126^\circ = 54^\circ$

Step2: Find ∠U

Sum of angles in a triangle is $180^\circ$:
$\angle U = 180^\circ - 65^\circ - 54^\circ = 61^\circ$

Step3: Match sides to opposite angles

In a triangle, shorter sides are opposite smaller angles:

• Smallest angle ($54^\circ$) → opposite $\overline{UV}$
• Middle angle ($61^\circ$) → opposite $\overline{VX}$
• Largest angle ($65^\circ$) → opposite $\overline{UX}$

Answer:

$\overline{UV} < \overline{VX} < \overline{UX}$